Barkley failed to secure a move away from Goodison Park on deadline day.
The 23-year-old had a medical at Chelsea but eventually opted against signing for Antonio Conte's side.
The Blues were prepared to pay £35m for Barkley, even though he is sidelined until November through injury.
And that ultimately put Tottenham off as they decided not to bid.
But according to the London Evening Standard, Spurs will look to secure a deal in January.
Despite Barkley preferring to link up with Mauricio Pochettino, Antonio Conte has not been discouraged from returning with another offer in mid-season.
Arsenal were also linked with interest in the England international midfielder.
The London Evening Standard add, though, that Spurs would be Barkley's ideal move ahead of Chelsea and Arsenal.
Barkley's refusal to sign a new contract means he will available on a free by next summer, meaning Everton must offload him in January.
Even still, his value will have decreased from the £35m Chelsea were set to pay.
Chelsea managed to get a £35m deal for midfielder Danny Drinkwater over the line last night.
Arsenal, meanwhile, failed to persuade £92m target Thomas Lemar to join and forced Alexis Sanchez to stay.
