This has led to them to set their sights on the United player, but it has been previously revealed that the Yorkshire outfit are holding out for up to £30m in order to sell.
Milan are yet to make a formal offer to the Blades for Souza, and it remains to be seen whether they would be willing to meet the £30m asking price set by the Championship club.
Souza has a contract with United until the summer of 2027, giving them a lot of leverage in any potential negotiations.
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But the situation surrounding their potential takeover could complicate the deal, with it being claimed that a consortium is looking to take a stake in the club.
AC Milan interested in Vini Souza
AC Milan are the latest club to join the race to try and sign Souza from Sheffield United this summer.
Fulham are also in the mix, and have reportedly already had a £15 million bid for the player rejected.
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The Cottagers are in the hunt for a replacement for Joao Pallinha, who made the switch to Bayern Munich already in this transfer window.
The Blades will be aiming to build a team capable of competing for automatic promotion next season.
Jamie Shackleton and Sam McCallum have already been signed, both joining as free agents after their departures from Leeds United and Norwich City, respectively.
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But their attempts to sign Harrison Burrows from Peterborough United have been hit by a snag due to the takeover situation, indicating a resolution may be needed before more additions are made.
The Blades have until 30th August to finalise any potential transfer moves before the market shuts for the calendar year.
Sheffield United’s £30m asking price for Vini Souza is unlikely to be met
Souza being sold for £30 million seems a very unlikely scenario this summer, especially since the Blades have been relegated.