Liverpool have also been heavily linked with a £8million move for Hull City left-back Andy Robertson, but the ECHO understands that is unlikely to materialise.
The Reds have scouted the Scotland international previously but they currently have no plans to follow up their interest.
There are a number of names ahead of Robertson and one of them is Sessegnon, who has enjoyed an outstanding breakthrough season in the Championship.
Fulham are reluctant to sell but their hopes of keeping him were dented by their play-off exit at the hands of Reading on Tuesday night.
Promotion to the Premier League may have convinced Sessegnon to stay put for a further 12 months, but now he will have a number of lucrative offers to make the leap into the top-flight.
Liverpool intend to be at the front of the queue with Jürgen Klopp believing he would be the ideal new recruit to compete with vice-captain James Milner for the left-back spot.
Sessegnon, who scored seven goals in 30 appearances for Fulham this term, celebrates his 17th birthday on Thursday.
Before the start of the season he pre-agreed his first professional contract with the Cottagers which will be activated on July 1.
Liverpool's final game of the season at home to Middlesbrough on Sunday is key to Klopp's summer transfer plans.
Victory would guarantee Champions League qualification and boost the manager's chances of landing targets such as Southampton centre-back Virgil van Dijk and Red Bull Leipzig midfielder Naby Keita.
Klopp is also keen to buy another top-class winger this summer.
Sadio Mane has been sorely missed since he suffered a season-ending knee injury last month and the German coach wants to ensure he has greater depth in that department in 2017-18.
Klopp had hoped to sign Julian Brandt from Bayer Leverkusen for around £25m but Liverpool are now looking at other options.
Brandt has made it clear that he would rather stay at Leverkusen for another year and play regularly than risk being a squad player at Anfield.
Long-standing target Christian Pulisic is also off the radar after he penned a new long-term contract with Borussia Dortmund.
Roma's Mohamed Salah is one of a number of other wide attackers across Europe under consideration.
Source: Liverpool Echo
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