According to Phil Kirkbride of the Liverpool Echo, the Blues want to add Barkley to their squad for the coming campaign, with manager Antonio Conte keen to increase the team's homegrown quota of players. As noted in the report, Danny Drinkwater and Alex Oxlade-Chamberlain have also been linked with Chelsea.
It's added that Everton value their midfielder at around £50 million, although Spurs are only ready to part with £20 million for the player.
Everton's high valuation is in spite of Barkley having one year left to run on his deal at Goodison Park. Per Kirkbride, Toffees manager Ronald Koeman has already confirmed the England international is poised to leave the club in this transfer window as he wants a "new challenge."
Although Everton have invested heavily this summer and appear set for an intriguing season, Barkley appears to see his future away from his boyhood club. The Liverpool-born midfielder is a product of the Toffees' academy and was expected to be the heartbeat of his local side for many years to come.
It appears that romantic scenario is unlikely, though, and the midfielder is on the cusp of a critical phase in his career.
Whichever club does end up getting the 23-year-old on board will have a talented footballer on their books. As we can see courtesy of Squawka Football, he's a creative player:
Additionally, Barkley is relatively versatile, strong on the ball and last season his work rate did improve under Koeman. The midfield is leaner and added a combative streak to his game that was absent while working with former manager Roberto Martinez.
What he needs to find is consistency. Too often in matches Barkley can go missing for spells, while his dallying in possession can be infuriating for supporters. Even so, with the right guidance, there is still time for him to blossom.
Conte may well be the type of figure Barkley needs. But the Uber Chelsea Twitter feed isn't overly keen on the idea of the Blues pursuing the Everton man:
If Barkley were to move to Stamford Bridge or Spurs in the current transfer window, his biggest challenge would be getting regular minutes on the pitch. It's tough to see him ousting any of Eden Hazard, Willian or Pedro at Chelsea, or Dele Alli, Christian Eriksen or Heung-Min Son at Tottenham.
For a footballer who is crying out for some regularity in his game, a role as a squad rotation player doesn't feel like the next step he needs.