The 18-year-old forward is highly regarded at Craven Cottage and has already featured for the first team under Scott Parker.
It remains to be seen whether the newly promoted club will consider allowing Jasper leave on loan ahead of the new season as Parker sizes up Fulham's return to the Premier League.
Sylvester Jasper is wanted by a number of Championship clubs on loan this season
Nevertheless, a host of top EFL sides are understood to be monitoring his situation, primarily ahead of the January window, in the event of the teenager being allowed to leave the club on a temporary basis.
Jasper, who is an England youth international, is viewed as a major talent at Fulham but the club may decide it will aid his development to leave on a short-term basis so he can play more regular senior football.
Jasper, who is contracted at the club until the summer of 2023, made his senior debut against Manchester City in January, and appeared twice in the league post-lockdown, against Brentford and Birmingham City.
He also set the Under-18 Premier League South alight last season, scoring nine goals and registering 10 assists in just 18 appearances during their title winning season.
Scott Parker rates him very highly and is weighing up whether to let him go out on loan
Consequently, Jasper was called upon by Under-23s throughout their 2019-2020 campaign. The 18-year-old scored twice in five PL2 appearances and featured in the EFL Trophy.
Jasper's impressive form saw Fulham hand the youngster a new three year deal at the club. Having put pen to paper, the Jasper said: 'I'm delighted to have signed a new contract with this great Club, especially after a great season for myself personally.
'And the Club winning promotion to the Premier League makes it even more special. My main focus now is to work hard and help the team any way I can to have a good season in the Prem.'