The 18-year-old is certain to leave Craven Cottage this summer, with the club’s relegation from the Premier League confirmed three weeks ago.
Fulham though want around £40million for the teenager, who has been brought back into the side by caretaker manager Scott Parker in recent games after an up and down season, and has shone in the wins over Everton and Bournemouth.
Tottenham have been tracking Sessegnon for some time and are favourites to land the winger with manager Mauricio Pochettino a big fan, but Manchester United, Liverpool and Paris Saint-Germain have also been linked with a player who will have only one year on his contract when this campaign ends.
However, Italian giants Juventus, keen to bring fresh blood into an ageing side which won the Serie A title at the weekend but flopped in the Champions League to Ajax last week, are now also monitoring Sessegnon and will make a summer bid.
Fulham now face a major battle to hold on to several of their major stars.
Parker said after the win at Bournemouth that he wants both Serbian striker Aleksandar Mitrovic and midfielder Tom Cairney to stay in order to build a squad to get out of the Championship next season.
The Cottagers may now offer both new deals in order to try to persuade each to stay.
But Mitrovic, valued at £30m by the club and only signed last summer, has already had offers from China, and West Ham and Crystal Palace are both interested.
Cairney still has four years of his current deal to run and is more likely to stay.
Turkish club Fenerbahce are though also interested in forward Ryan Babel.
Parker’s chances of landing the manager’s job full time in the summer have been boosted by the wins over Everton and Bournemouth – but the club have also looked at Celtic manager Neil Lennon as a possible appointment.