Coutinho is said to have handed in a transfer request as the Brazilian looks to force a move to Barcelona, although Klopp claimed on Saturday that he was still confident of keeping the attacker on Merseyside.
That said, according to The Mirror, Klopp is aware that Coutinho could leave for Spain, and the Liverpool head coach has identified Insigne and Meyer as potential replacements.
Insigne scored 20 times for Napoli during the 2016-17 campaign, and the report claims that Liverpool would be prepared to pay up to £60m in order to sign the 26-year-old in this summer's transfer window.
Meyer, meanwhile, is also said to be a target with the highly-rated German, who has previously been linked with a move to Tottenham Hotspur, out of contract at Schalke next summer.
Liverpool opened their 2017-18 Premier League campaign with a 3-3 draw against Watford on Saturday afternoon.