The 16-year-old has caught the eye with some impressive performances for the Championship side this season, and the Craven Cottage club are believed to be holding out for a £15 million fee should they decide to sell, per Greg Stobart of Squawka.
The report added Sessegnon will consider his future, but Premier League clubs may be put off by the high price Fulham are demanding.
The left-back has caught the eye with his emergence from the Fulham youth ranks and has featured eight times in the starting lineup in the Championship.
He has also come to prominence by scoring in successive FA Cup games to help Slavisa Jokanovic's side reach the fifth-round stage, where they face an intriguing home tie against Spurs on Feb. 19, who are likely to get an up-close look at Sessegnon.
At 16, Sessegnon's winning goal against Cardiff City in the third round saw him become one of the youngest scorers in the competition's history. It prompted his manager to label him one of the most talented teenagers in England, per Sky Sports.
Jokanovic said: "I am sure that he is going to be a very important player for us in the future. But he's only 16 years old, we have to be careful with him, and I prefer not to talk so much about Ryan Sessegnon. He's a very intelligent kid, he's working very hard and has to keep going."
Sessegnon is a clear prospect who could become a real attacking force if his development continues apace and he adds match experience and increased strength to his slight frame.
With four goals this season, he has proved he has an eye for a finish and has showed useful versatility in midfield along with his appearances in the Cottagers' back line.
OptaJoe referenced the significance of Sessegnon's goal against Cardiff in the Championship on Aug. 20, 2016:
Liverpool's reported interest in the Fulham youngster perhaps comes as little surprise.
Manager Jurgen Klopp has made midfielder James Milner his first-choice left-back this campaign, but despite the former England international's dependability, the German boss is likely to eventually prefer a natural left-sided player who can add better balance to his side, a role Sessegnon could feasibly grow into.
Should Spurs rival Liverpool for Sessegnon's signature, they can hold up the example of the progress made by Danny Rose in the left-back position at the north London club.
Rose has developed under the guidance of boss Mauricio Pochettino, both defensively and particularly as an attacking wide player over the past two seasons.
Pochettino's apparent readiness to hand young players first-team opportunities may appeal to Sessegnon should he decide his future lies away from Fulham.