According to Ed Aarons of the Guardian, the Red Devils are one of a number of clubs impressed by the development of the 17-year-old, with Tottenham Hotspur and Real Madrid also said to be keen on the £30 million-rated left-back.
It's said United manager Jose Mourinho would be willing to allow Luke Shaw to leave Old Trafford in January in order to make room for Sessegnon in his squad. The former Southampton man has made just one Premier League start in 2017-18.
"Should United have a bid accepted, Tottenham are expected to renew their approach but have also enquired about Shaw," added Aarons. Spurs are also reported to have had an offer of around £20 million rejected for the Fulham tyro in the summer.
The interest in Sessegnon is understandable, as he's made rapid progress in English football's second tier.
Sports journalist Ryan Baldi envisages an exciting trajectory for the teenager:
Sessegnon has been a regular for the London club since he was 16, showing remarkable maturity to excel in a physical division.
Whether operating as a left-back, a wing-back or even a winger, the youngster typically lights up a football match. He boasts blistering pace and has showcased a coolness in the final third that typically escapes young players.
That talent was on show earlier in the season when Fulham beat Sheffield United 5-4 and Sessegnon sealed a hat-trick.
Per OptaJoe, he followed in the footsteps of one of England's most exciting prospects:
Given the strides he has made so early in his football career, there will be a lot of clubs keen to win the race for Sessegnon's signature.
United would benefit from having someone like him around. They've struggled to find a consistent left-back, with Ashley Young, a makeshift option, filling in for most of the campaign. Marcos Rojo, Daley Blind and Matteo Darmian have all failed to convince when tried there.
The man many at Old Trafford had been pinning their hopes on was Shaw, although it appears his career at United may be nearing its end.
Journalist Yousef Teclab believes Sessegnon can learn lessons from the former Southampton man:
Indeed, a move midseason would be a major gamble, as Sessegnon would be thrust into a cut-throat environment. The Championship is notoriously difficult, although the top end of the Premier League would represent a major culture shock for somebody so young.
It's why the sensible decision would be to stay at Fulham, for the rest of the campaign at least. Provided he keeps developing and gaining crucial experience, the illustrious interest that has emerged will still be there at the end of the campaign.