The Cottagers are believed to have already seen two bids rejected by the Red Devils for the Scotland international, whom they have identified as an ideal replacement for Joao Palhinha.
Fulham's second offer for McTominay was supposedly in the region of £20m, and the Cottagers turned their attention to other targets after failing with that approach earlier this month.
Since Man United last turned away Marco Silva's side, Serie A giants Napoli have joined the race to sign McTominay, as confirmed by their sporting director Giovanni Manna over the weekend.
However, according to Sky Sports News reporter Dharmesh Sheth, Fulham have quickly rekindled their interest in the 27-year-old, and Man United are braced to receive a third bid from the London club.
Sheth reports that Fulham restarted conversations with Man United over a deal, and the Cottagers will submit an improved offer if negotiations with Erik ten Hag's side are positive.
Fulham were supposedly not prepared to try again unless Man United indicated that they would be willing to relent on their asking price, thought to be in the region of £30m.
The Red Devils are at risk of losing McTominay for nothing in 2025, as he is now in the last 12 months of his contract, but the club can trigger a one-year extension to protect his value.
However, a long-term renewal is not thought to be in the pipeline, so Man United could very well activate his contract option in January - as they have often done with other players in the past - if no move can be agreed this summer.
McTominay has been with the Red Devils since 2002 and has registered 29 goals and eight assists in 254 appearances for the club in all competitions, albeit while failing to become an undisputed starter.
Is there a future at Man United for McTominay?
When Man United were in desperate need of a goal last season, McTominay would often be the man to provide it, netting a career-best 10 goals in all tournaments during the 2023-24 campaign, including seven in the Premier League.
The 27-year-old's output in the final third makes him an intriguing option further forward, and Ten Hag is believed to be happy to keep McTominay around for the 2024-25 season.
However, the midfielder failed to make the first XI for either the Community Shield loss to Manchester City or opening Premier League success over Fulham, only getting six minutes off the bench against the latter.
Casemiro and Kobbie Mainoo are Ten Hag's first-choice lynchpins when fully fit, and McTominay would fall further down the pecking order if either Sander Berge or Manuel Ugarte arrives in the last knockings of the window.
Joshua Zirkzee's arrival and Mason Mount's return to fitness will also restrict McTominay's minutes in an advanced role, so his 22-year Man United career may have finally run its course.