The left-back signed his first professional contract with Fulham in June after making the breakthrough at the Championship club last season.
Sessegnon is, despite the strong interest from Spurs, with the Fulham squad for Tuesday evening's Championship clash against Leeds United.
Goal understands that Mauricio Pochettino's side are also targeting his twin brother Steven in what would be a double deal.
Fulham have ambitions to return to the Premier League and they see Sessegnon as a key part of their promotion bid that has seen them start the season with two draws.
Sessegnon's value is expected to continue to grow amid interest from England's top flight and Fulham haven't been put under any pressure from the player to force through a sale.
Tottenham have yet to make a signing in the summer transfer window but are chasing reinforcements in the full-back positions, with Kieran Trippier and Danny Rose currently out injured.