A deal likely to be completed next week, says the Daily Express.
Tottenham have already made two high profile signings so far this summer with Tanguy Ndombele and Jack Clarke joining for £53.8million and £11m respectively.
After a period of almost two years without making any additions to their first team squad, Spurs are set to add another promising youngster to their ranks.
Sessegnon has been a Fulham player since 2008 when he joined as an eight-year-old, before making his first-team debut in 2016.
The 19-year-old stole the headlines in the 2017/18 campaign when he was named EFL Championship Player of the Season after scoring 15 goals to fire Fulham to promotion.