Wan-Bissaka has only one year remaining on his contract, and United are believed to prefer to sell him this summer rather than risk losing him for free at the end of the 2024-25 season.
Acquired from Crystal Palace in 2019 for around £45m, the right-back has been a dependable performer for the Red Devils over the last five years.
However, he has fallen behind Diogo Dalot in Erik ten Hag's pecking order and has been heavily linked with a move to West Ham this summer.
However, his potential move to the London Stadium now seems likely to be delayed, with the Serie A champions believed to be looking to hijack the move before the start of the new season.
Inter Milan plot Wan-Bissaka transfer hijack
West Ham chief Tim Steidten has reportedly been negotiating with Man United over a small difference in valuation between the two clubs regarding the final transfer fee for the full-back.
Several reports in recent days have suggested that the player has already agreed to a five-year contract to join the Hammers this summer.
However, according to Football Insider, it now appears that Simone Inzaghi's side have thrown a spanner in the works by stepping up their efforts to secure the 26-year-old a move to the Serie A.
The report adds that the Italian league champions have reached out to the Red Devils about negotiating a deal, as Wan-Bissaka is said to prefer a move abroad rather than remain in the Premier League.
It is understood that the decision now rests with Wan-Bissaka, with United being happy to allow him to leave for a fee of around £18m. West Ham reportedly made an opening offer of £10m for the Englishman.
The Hammers are believed to have identified the 26-year-old as a target after losing Ben Johnson a free transfer at the end of last season.
More defensive reinforcements expected at Old Trafford
Man United faced major setbacks in defence last season with all of Luke Shaw, Tyrell Malacia, Harry Maguire, Jonny Evans and Lisandro Martinez spending time sidelined through injury.
Thus strengthening at the back has been one of the Red Devils' main priorities this summer and they have already made progress in that regard with the signing of Leny Yoro last month.
However, it seems United are not done yet, with reports suggesting that the club have now made formal offers for Bayern Munich duo Matthijs de Ligt and Noussair Mazraoui.
De Ligt has been linked with a move to Old Trafford for the majority of the summer, while Mazraoui has emerged as a potential replacement for Wan-Bissaka.
Both players are believed to have agreed to personal terms with the Premier League giants after being made aware that they are not a part of Bayern's long-term plans under new manager Vincent Kompany.