The England international usurped Liverpool's Virgil van Dijk as the most expensive defender in football history when he moved to Old Trafford in an £80m deal during the most recent transfer window.
Maguire has made an assured start to life at the club, and Vidic is confident that more is still to come from him despite admitting that the defence as a whole does still need improvement.
"I think he's had a pretty good start. Obviously we have big expectations of him, he was a big signing," Vidic is quoted as saying by the Daily Mail.
"If you want to win trophies, you need to have a strong defence, don't lose many goals. Obviously he's still new. He just came, he didn't have a pre-season with the team. I think better games are coming from him and I think he'll be a good signing.
"We need the defence to improve, we all know how important the defence is in winning trophies."
Maguire has started all five of United's Premier League games so far this season, helping his side to keep two clean sheets.
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Nemanja Vidic tips Harry Maguire to shine at Manchester United
Former England and Newcastle forward Peter Beardsley will seek to return to the sport once he has served a 32-week suspension from all football-related activity after being found guilty of making racist comments.
The 58-year-old, who has denied the allegations, left his role as Newcastle's Under-23s coach earlier this year following an internal investigation.
After being subsequently charged by the Football Association for an 'aggravated breach' under FA Rule E3(2) due to reference of ethnic origin and/or colour and/or race and/or nationality, which was then followed by an independent regulatory commission hearing, Beardsley will now not be able to return to working in football until April 2020.
The regulatory commission's written reasons for its decision have been published in a 42-page document covering the three-day hearing at Wembley in July.
The three-person commission accepted allegations made by four unnamed players that Beardsley had told black players of African origin that "You should be used to that" during a team-building exercise at Go Ape, suggested 18-year-old players were older than they claimed and called another a monkey.
As well as the suspension, the FA has ordered Beardsley to complete a face-to-face education course – with the commission adding it was "satisfied that Mr Beardsley is not a racist", but stating his comments were "wholly unacceptable".
In a lengthy statement released on his behalf by his solicitors, Beardsley spoke of his disappointment at the decision, but vowed to return to football.
"Peter Beardsley is very surprised and disappointed by the decision of the Regulatory Commission," a statement read.
"It was almost impossible for Peter to clear his name because of the serious flaws and contamination of evidence that occurred in the disciplinary process before Newcastle United and by the unusual fact that the FA rules put the burden of proof on him to prove his innocence in the proceedings.
"After a long process which has been unnecessarily protracted, Peter feels vindicated that the commission has expressly found that he is not a racist."
Beardsley had, the statement added, been "inundated with support from all over the country", which included from the likes of John Barnes, Kevin Keegan, Les Ferdinand and Andrew Cole to provide "unchallenged evidence" over his "good character, the fact that he is not a racist and whatever was said, there was no intent to cause offence".
The statement referenced Beardsley's affection for the club and its fans, but also pointed out a lack of "relevant training and education" from Newcastle, saying the former striker had "always been willing and eager to attend" any such sessions.
"Peter has categorically denied the allegations throughout whilst continuing to honour the contractual obligations of confidentiality to Newcastle United and maintaining his silence which in itself has been very difficult," the statement said.
"With no avenue left open to him to clear his name Peter has no choice but to acknowledge the decision and now looks forward to moving on with his life and resuming his career.
"He shall respect the sanction imposed and looks forward to returning to work in football, which has been his life, at the end of his suspension."
In January 2018, a formal complaint was made about Beardsley by midfielder Yasin Ben El-Mhanni, who has since left Newcastle. Beardsley had always denied the allegations.
Nevertheless, the commission eventually ruled against him.
"We regret the outcome that we have felt compelled to reach in this case. Mr Beardsley is a towering figure in football and his footballing reputation is beyond question," the commission said in its findings.
"But on the three occasions which are the subject of the charges, he made remarks which were obviously racist and were wholly unacceptable. Even if he did not intend to do so, he plainly did cause offence.
"It is particularly important at a time when racism in football is prevalent that remarks of the kind made by Mr Beardsley are punished severely."
The written reasons also said Beardsley contended that three of the black players had "made up the allegations motivated by financial greed, and implicating the agent of two of them, for which he did not have a shred of evidence."
Beardsley's leading counsel was Nick De Marco QC, who told the commission the former player had found it impossible to secure income from football 'punditry' or other employment while the charges were hanging over him.
The 58-year-old's "exemplary" disciplinary record was also noted, having never been subject to any charge before.
Under the 'mitigating factors', it was stated the commission were "satisfied that Mr Beardsley is not a racist in the sense of being ill-disposed to persons on grounds of their race or ethnicity."
The lack of "training and education about offensive racist remarks and the importance of not making them" for Beardsley was also documented.
However, the commission also added if Beardsley had accepted the charges and "apologised for his behaviour, that would have afforded him considerable mitigation. By fighting the case, he has lost the benefit of that".
The FA had also invited the commission to impose a "financial penalty", which was decided would not be appropriate in this case, although Beardsley was directed to pay the Regulatory Commission's costs for the three-day witness hearing.
Although his solicitors confirmed the matter would not be pursued any further, under FA regulations Beardsley was entitled to an appeal.
Anti-discrimination body Kick It Out later released a statement urging Newcastle to reveal the results of their own investigation and "clarify whether he was sacked for racist abuse".
The statement read: "The racist comments and innuendoes made by Peter Beardsley were appalling and he is rightly facing an appropriate eight-month ban, as well as mandatory education.
"Beardsley's career in football has no relevance to this case – calling black players monkeys, comparing black players to apes and questioning their true age are all horrific racial stereotypes and regardless of their reputation. Punishment and education is the only way to deal with these matters.
"Now Beardsley has been found guilty, we once again reiterate our call that Newcastle United should publish the result of their own investigation, and clarify whether he was sacked for racist abuse. This inaction dilutes the club's message and brand of #UnitedAsOne."