Tottenham have been trying to sign Sessegnon all summer and have now offered £30m plus midfielder Josh Onomah in an attempt to convince Fulham.
Spurs boss Mauricio Pochettino considers the teenager as one of his main targets this summer, and it is understood that this latest offer can get over the line before the transfer deadline day on Thursday.
The 19-year-old himself is keen on a move to the Premier League and would be happy to see the deal go through.
Sessegnon is one of the top rising talents in English football and was part of the England squad during this summer’s Euro U-21 championship.
Since his debut when he just aged 16 years old, Sessegnon scored 21 goals in 75 appearances for Fulham. He struggled to impress upon Fulham’s return to the top-flight last season as he registered just two goals in 35 games.