The England international almost completed a deadline day move to Chelsea in August, only for the deal to fall through in the closing stages of the window.
Spurs were also interested in signing the Everton midfielder but a move failed to materialise.
Mauricio Pochettino wants more options in midfield to support Eric Dier, Victor Wanyama and Mousa Dembele, who is currently struggling with a foot injury.
And according to the Daily Mirror, both Premier League outfits will return with bids for Barkley in January.
The 24-year-old is still recovering from a pre-season hamstring injury and is not expected back until the New Year, although it looks as if his Everton career is all but over.
Barkley turned down a new £100,000-a-week deal at the Merseyside outfit, as he desires a move to a bigger club.
And with his current contract at Goodison Park expiring in 2018, Everton are likely to sell for a cut price, rather than lose the star for free next summer.
Barkley will be hoping to secure first team football quickly upon his return from injury, with places up for grabs in Gareth Southgate's England World Cup squad.
The Three Lions chief is lacking in the central midfield area, meaning a run of games under his belt is likely to lead to Barkley's inclusion in Russia next year.
Spurs already boast a wealth of young English players within their ranks, with Harry Kane, Dele Alli, Kieran Trippier and Harry Winks all included in this week's England squad.
