According to Jack Wilson of the Daily Express, Manchester United, Tottenham Hotspur and Chelsea have been keeping an eye on the development of the 17-year-old, who has been tearing up the Championship with his dazzling performances.
However, it's suggested that if the England youth international is to move on in the summer, then Anfield would be his preferred choice.
"It's understood from sources close to the player that a move to Anfield is something Sessegnon would be keen on if Fulham don't win promotion," Wilson said. "Playing under Jurgen Klopp appeals to the youngster, who grew up a boyhood Liverpool fan."
Sessegnon burst on to the scene last season with some accomplished performances, although he's moved into another gear this term.
As noted by This is Anfield's Jack Lusby, while he's played at left-back in the past, the youngster has been blossoming in a more advanced position in 2017-18:
Sessegnon has thrived for Fulham and is the driving force behind the team's promotion push with his exemplary efforts on the wing.
The teenager uses his pace to unsettle defences with surges from out to in. When on the ball, Sessegnon is able to glide past opposition players and get fierce deliveries into the box.
It's his composure that separates the left-sided star from many players of his age, though. While some upstarts will snatch at chances and panic in the final third, Sessegnon has showcased a remarkable coolness when he's in dangerous positions.
Interest in Sessegnon is inevitable in the summer given just how impressive he has been. Fulham supporters will be hopeful that Premier League football will convince him to stick around.
What is important is that he moves to a club where he will continue getting regular minutes, as the 17-year-old has already showed enough to suggest he's capable of stepping up to the top flight.
However, Sessegnon appears to have a mature head on his young shoulders, and given how rapid his development has been at Fulham, perhaps he won't be in a rush to move on just yet.