The 18-year-old is expected to be the subject of formal offers once the summer transfer window swings open.
He has been linked with leading sides across Europe for some time, with Manchester United said to be among his many suitors.
With Fulham having suffered relegation out of the Premier League, Sessegnon finds himself at an important career crossroads.
His current contract is due to expire in 2020 and if no fresh terms are agreed, then the Cottagers will have little choice but to cash in on a prized asset while they are still able to demand a fee.
Sessegnon is giving little away when it comes to his plans, though, with the England U21 international keeping his cards close to his chest.
He has told Sky Sports when quizzed on the exit talk: "I'm still a Fulham player, contracted until 2020.
"So I'm still a Fulham player and in terms of that, that's all I can say at the moment."
Transfer speculation around Sessegnon quietened earlier in the season as he lost his place in the Fulham side under Claudio Ranieri.
He has, however, returned to prominence since Scott Parker took the reins at Craven Cottage.
A highly-rated talent is enjoying his football again, despite slipping through the top-flight trapdoor, and believes the Cottagers should keep faith with the man currently at the helm.
"When he [Parker] was a player he was such an intelligent player," Sessegnon said.
"And he's just brought his knowledge of his playing time into management really.
"Everyone just wants to play for him. Everyone respects him highly at the club and when you respect someone so highly it's easy to get everyone motivated for games.
"I think he's the right man to bring this club back to the Premier League."
Fulham have three more fixtures to take in before returning to the Championship, with a home date against Cardiff on Saturday set to be followed by a trip to Wolves and a final day showdown with Newcastle in west London.