The England international, who has 22 caps under his belt, is yet to play for the club this season because of a severe hamstring injury.
The 24-year-old is nearing full fitness again, and it could lead to a bidding war between the two London clubs.
The report adds that Everton are resigned to losing the England midfielder, who was on the verge of a £25 million transfer move to Chelsea just hours before the summer transfer window closed. The deal collapsed at the last minute.
Spurs have a strong attacking midfield unit, but Barkley could still be a fantastic addition for the north London club.
The report adds that Spurs have decided to enter the bidding process, believing they can pull off the final deal.
Meanwhile, Everton are close to completing the singing of Cenk Tosun, and are showing strong interest in bringing Sevilla’s Steven N’Zonzi to Goodison Park.