The 25-year-old is understood to be closing in on a move to Antonio Conte's side, who have now reached an agreement in principle over a fee for his services.
Richarlison is also believed to have agreed personal terms with the Lilywhites, which would bring an end to his spell at Goodison Park four years after arriving from Watford.
According to journalist Bruno Andrade, Richarlison has already undergone his medical tests with Tottenham and is now poised to sign a five-year contract in the English capital.
A separate report from The Athletic states that Tottenham quickly struck a deal with Everton for the signing of Richarlison, who will cost the North London club an initial £50m.
The report adds that Tottenham could end up forking out an extra £10m in performance-related add-ons, and the Brazil international is keen to test himself in European competition.
However, the two clubs are yet to sort out the final terms of the payment structure, but Everton are under pressure to make a big-money sale within the next 24 hours.
Should the Toffees fail to raise funds before Friday, the club are at risk of punishment for failing to meet the Premier League's profit and sustainability rules criteria.
As a result, Tottenham are hopeful of concluding a deal to sign Richarlison before the weekend, and he would become Conte's fourth signing of the summer window.
The former Fluminense youngster cost Everton an initial £35m to sign from Watford in 2018, and he has registered 53 goals and 14 assists in 152 appearances for Everton across all competitions.
Richarlison found the back of the net 10 times and provided five assists in 30 Premier League games last season to help the Toffees retain their top-flight status, but he has only finished as high as eighth during his time on Merseyside.
Nevertheless, former Tottenham and current Everton winger Andros Townsend does not believe that the Lilywhites represent a "step-up" for Richarlison, telling talkSPORT: "I think you're being slightly disrespectful by calling Spurs a step-up.
"I think Everton is one of the biggest clubs in England, one of the most historic clubs, one of the biggest fanbases. He's already a hero at Everton for what he's done. He's a fantastic player and towards the end of the season the goals he scored to keep us up."
Should Richarlison complete a £50m transfer to Tottenham, he would become Conte's fourth signing of the summer window after Ivan Perisic, Fraser Forster and Yves Bissouma.
Conte will likely turn his attentions to bolstering his side's defence once a move for Richarlison is finalised, and Spurs are said to have agreed a deal to sign Barcelona centre-back Clement Lenglet on a season-long loan.