Sessegnon, 17, is the hottest prospect in English football thanks to his stunning form for the Championship outfit.
The Premier League’s biggest clubs are tracking his progress but the Red Devils plan to win the race for his signature when the transfer window reopens.
United have been monitoring Sessegnon since he broke into the Fulham team at the start of last season.
They reportedly stepped up their efforts to sign the England youth star after he scored a hat-trick in last month’s 5-4 win at Sheffield United.
And, according to The Sun, Mourinho is ready to bid £25million before allowing Sessegnon to see out the season with Fulham.
Luke Shaw’s return to the fold has eased Mourinho’s plan to strengthen the left-side of his team next month.
Sessegnon has mostly featured at left-back for Fulham but his best performances have come on the left-wing.
The Roehampton-born wonderkid has scored four goals and provided two assists in 23 appearances for Slavisa Jokanovic’s side this term.
Jokanovic is “confident” of keeping Sessegnon and has urged the club not to cash in.
“If we want to be competitive we must keep our important players,” he said.
“All the questions are what the value of this player is, but myself, as a coach, I prefer to stay with the more important players for the competition that is ahead of us, but on the other side I can understand the business side too.
“In this moment, I am not thinking of being without him for the season, but it is not under my control.”
Sessegnon became the first professional footballer in English football to have been born in the 2000s to score a goal when he netted against Cardiff City in August 2016.
He was named in last season’s Championship Team of the Year and helped England’s Under-19s to European Championship glory in July.