Manchester United reportedly failed in an attempt to sign Mats Hummels from Bayern Munich earlier this summer.
The 30-year-old was made available for transfer at the end of the most recent campaign, and the defender has now rejoined Borussia Dortmund after a three-year spell in Munich.
However, according to Bild, United were prepared to offer the Germany international a more lucrative contract to make the switch to Old Trafford.
The report claims that Hummels rejected a transfer to the Premier League giants due to their failure to qualify for next season's Champions League.
Ole Gunnar Solskjaer is keen to bring in another centre-back, although reports have suggested that United are being hampered by a restrictive transfer budget.