The recently-relegated side have previous fended off interest in the 19-year-old, but The Telegraph reports that there has been a breakthrough in talks between the two clubs.
Spurs are thought to pay around £20m plus odd-ons to sign Sessegnon, who has one year left on his current Fulham contract.
Sessegnon joined Fulham aged eight and The Independent understands that Fulham have anticipated his exit for six months and will not stand in his way if he wishes to leave.
Tottenham are highly unlikely to make a move for Real Madrid outcast Gareth Bale.
Real Madrid manager Zinedine Zidane said his exit from the Spanish capital would be “good for everything”, which provoked Bale’s agent to call the Frenchman a “disgrace”.
The Independent recently revealed that Tottenham are showing tentative interest in the player that left them in 2013, although Spurs are not willing to even get close to Bale’s enormous wages.
Spurs have been beaten to signing Real Madrid midfielder Dani Ceballos on loan for the season by north London rivals Tottenham.
It had been reported that Nabil Fekir was on the verge of joining Real Betis, but now he could be tempted to leave Lyon for Napoli.
A deal to Real Betis may help Tottenham in their attempts to sign Betis midfielder Giovani Lo Celso, who Fekir was going to replace. With Betis perhaps out of the hunt for him, Lo Celso's exit looks slightly less likely.
Mauricio Pochettino is said to be a keen admirer of the £54-rated midfielder, who could be a good replacement for Christian Eriksen.
Spanish outlet AS reports that Tottenham have offered Eriksen to Atletico Madrid for €60-70m.
The same report also claims that a Spurs representative met with Miguel Angel Gil, Atletico’s CEO to discuss a potential deal.
Following Tottenham’s defeat in the Champions League final, Eriksen said: “I feel that I am at a stage of my career where I would like to try something new.”
It looks as if Toby Alderweireld is ready to commit his future to Tottenham after he revealed he expects to start the season with Spurs. “Yes. That’s my focus in football,” he said when quizzed about whether he’d be wearing a Tottenham shirt in another competitive game. “Everything can go quick but all I’m doing is focusing on Spurs and being fit for the start of the season.”