Sky Sports is reporting that the Red Devils remain keen on a deal to bring the 19-year-old left-sided player to Old Trafford this summer.
The same story says that both Tottenham Hotspur and Juventus are also interested in the teenager ahead of the summer transfer window.
According to the same article, Sessegnon is reluctant to play another season in the Championship after Fulham were relegated from the Premier League this term.
The same story also says that there is a sense of acceptance at Fulham that the time may be right to let Sessegnon move on and leave the club.
Sessegnon was a consistent performer for Fulham this season, scoring two goals and making six assists in 35 Premier League games.
Manchester United are bound to be linked with a host of top players this summer as they look to rebuild after a disappointing campaign.
The Red Devils ended up in sixth place in the Premier League table and without a trophy for the second season running.
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