The Daily Express is reporting that the Red Devils are keen on a move to bring the 18-year-old left-sided player to Old Trafford as they look to strengthen their squad ahead of next season.
The same story reports that Sessegnon is stalling on a new contract at Craven Cottage and Manchester United have noted that talks are not going well between the two parties.
The England Under-21 international has 18 months left on his current deal with the Cottagers and that could mean that his transfer fee could be reduced this summer.
According to the same story, Sessegnon will be reluctant to stay at Fulham if the Cottagers are relegated to the Championship this season.
The 18-year-old has been in good form this season and has scored two goals and made five assists in 23 Premier League games this term.
Meanwhile, Manchester United are currently preparing for their crunch Champions League last 16 clash against Paris Saint-Germain at Old Trafford on Tuesday night.
The Red Devils were 3-0 winners at Fulham on Saturday in the Premier League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news