Barkley, who is out injured at the moment, is out of contract at the Toffees at the end of the season.
It has been reported that the England international has told Everton chiefs that he could stay and sign a new long-term deal at the club.
A report in Bleacher Report has claimed that Tottenham would be willing to offer around £15 million for Barkley in the January transfer window.
Barkley is a very talented attacking midfielder, and with Everton struggling at the moment, him committing his long-term future at Goodison Park would be a massive boost to the Toffees.
Spurs have a strong midfield, and the 23-year-old would struggle to play regularly for Mauricio Pochettino’s side.