The Red Devils boss is ready to take advantage of those cash-flow problems with a bid for the central defender who only arrived from Juventus last summer.
Milan need to raise around £45m before the transfer window closes and Bonucci is a player they are willing to part with.
Bonucci quit Juve last summer after their disastrous Champions League final defeat to Real Madrid in Cardiff.
His arrival at the San Siro was expected to bring a new era of success to a historic club that has hit hard times in recent years.
Bonucci was part of a £150m net spending spree that proved to be a disaster, with Milan finishing sixth in Serie A having sacked manager Vincenzo Montella.
Gennaro Gattuso managed to steady the ship but Milan’s financial woes have rumbled on into the summer.
Investors Elliott Management took over the club this month after Milan’s Chinese owners failed to repay a debt of £28m (€32m).
Meanwhile, Manchester United are set to sell Dutch defender Daley Blind back to his former club Ajax for an initial £14.1m, which could become £18.5m with add-ons.
Transfer round-up
EVERTON are confident that they have done enough to see off Leicester and West Ham in the race for Barcelona’s Colombian World Cup star Yerry Mina.
Central defender Mina, 23, who caught the eye at the World Cup, scoring Colombia’s equaliser against England, wants to quit Barca because of a lack of first team opportunities.
CRYSTAL PALACE will this week follow up their interest in Michail Antonio, with West Ham needing to balance their books after some heavy spending.
The Hammers will allow Antonio to make the switch across the capital for around £15m after splashing out around £90m.
BOURNEMOUTH boss Eddie Howe is eying a £25m double swoop on Championship side Brentford for Ollie Watkins and Chris Mepham.
The Cherries, who have already had a £10m bid rejected for central defender Mepham, 20, will raise their offer to around £12.5m, with a similar bid planned for Watkins, 22, who is a left winger.
TOTTENHAM midfielder Mousa Dembele has been told by Inter Milan that they want to know this week if he is interested in accepting their offer of a £13m move to Italy.
The Belgian international only has a year to run on his Spurs deal but wants to take his time before deciding where he wants to be playing next season.