Chelsea, Tottenham, Arsenal, Liverpool and the Manchester clubs are among the heavyweights who are monitoring the 16-year-old, who has made 24 appearances for Fulham this season.
Slavisa Jokanovic’s side are battling for a playoff spot in the Championship and currently sit just a point behind Sheffield Wednesday in sixth position.
And Sessegnon wants to spur the Cottagers to the Premier League without becoming too concerned with interest from further afield.
“My ambition is to be the best I can be,” Sessegnon told FulhamFCTV. “I am a Fulham player, this is my club, I love being at this club.
“The opportunities I have had this season have been great and on a personal note I just want to help the team gain promotion to the Premier League where we belong.
“I don’t pay too much attention to it [the talk in the press] I just focus on one job and that is playing for Fulham.”
Sessegnon has been an increasingly regular presence among Jokanovic’s promotion-chasers after making his debut in the 3-2 EFL Cup win over Leyton Orient in August.
Undoubtedly his best performance yet came in a 3-1 win at Newcastle earlier this month where he scored twice.
“I am surprised how many games I have played with the first team at the age of 16, but it has been fantastic so far and I just want to keep on going,” Sessegnon added.
“I did set myself a target, at first I did say five to ten games just to be involved, but as it has gone on I have been more and more part of the squad and I just want to keep going.”