The midfielder is primed to complete a move from Brighton and Hove Albion to Spurs for a fee of £25 million.
Bissouma has long been regarded as one of the best engine-room operators outside the top six.
However, Bissouma’s prospective switch to Spurs may benefit Everton.
The Toffees are reportedly targeting Harry Winks and Bissouma’s arrivals could see him offloaded by Conte.
Winks, 26, fell down the pecking order at Tottenham towards the end of the 2021-22 season.
He did not start a Premier League game after 26 February. Winks made six substitute cameos and was left on the bench seven times during that period.
Everton are likely to be in the market for a midfielder this summer.
Fabian Delph has been released while Donny van de Beek has gone back to Manchester United following his loan spell at Goodison Park during the second half of the campaign.
The Blues currently have Abdoulaye Doucoure, Allan, Tom Davies and Jean Philippe-Gbamin - who has returned from his stint at CSK Moscow - as holding-midfield options.