According to Dan Kilpatrick of the Evening Standard, the Cottagers want to get him tied down for the long term as the 18-year-old has less than two years left on his current deal.
It's added Spurs have long been admirers of the England youth international, while the Red Devils have also been credited as showing an interest.
"Both Tottenham and Manchester United showed strong interest in Sessegnon, while Spurs also looked at a deal to take Ryan's twin, Steven, to north London along with his brother," Kilpatrick noted. "Tottenham are thought to have enquired about Sessegnon in each of the last two summers."
It's added that Sessegnon showed his commitment to Fulham by agreeing professional terms when he was 17, despite the fact a number of European football's biggest names were keen to acquire him then. The youngster has been vindicated in the decision he made.
Sessegnon has continued to get games in the Fulham first team and had an excellent year in 2017-18, helping the Craven Cottage club earn promotion to the Premier League.
Despite his tender years, the England youth star was a regular in the team and relished the attacking responsibility placed on his shoulders when pushed into a more advanced position, per Squawka Football:
While there was some tentative talk about Sessegnon going to the FIFA World Cup with England and some expectations he may be able to take the Premier League by storm, things have unsurprisingly slowed down for the versatile star.
Despite starting the first two games of the campaign for Fulham, Sessegnon has been left on the bench for the last two matches. The team have fared well without him, too, beating Burnley 4-2 in a game Sessegnon only played a minute in and drawing 2-2 against Brighton & Hove Albion in which the youngster was a late substitute.
Still, it's understandable Fulham have sought to keep the left-footer out of the spotlight for a spell, and it feels inevitable Sessegnon will have a role to play at some stage later in the season.
Journalist Seb Stafford-Bloor has been impressed with some of the glimpses we've seen from the player:
Given the maturity, intelligence and technical ability Sessegnon has shown this early in his career, the high-profile interest is natural. However, it seems sensible for him to stick around at Fulham for the time being.