All parties are believed to be hopeful a deal can be concluded for the 19-year-old before the transfer window closes on Thursday.
The versatile left-sided player is a long-term target for Mauricio Pochettino, who has already added Tanguy Ndombele to his squad this summer in a record-breaking deal for the club.
Sessegnon has returned to the Championship with Fulham this season following their relegation from the Premier League.
He scored two goals and assisted six more last season in what was his debut top-flight campaign.
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