According to MailOnline's Matt Barlow, Barkley snubbed a move to Chelsea in the summer as he preferred a switch to Tottenham Hotspur, but the Blues are preparing to go in for the Englishman again after Spurs did not sign him at the start of the season.
Chelsea could still have a fight on their hands with their London rivals over Barkley, though, as Tottenham manager Mauricio Pochettino has hinted he could be keen to snap him up, per Barlow: "We are focused on trying to bring more English players through the academy. If we don't have this profile we will try to take advantage of the English market and add more English players here."
Barkley, 24, has yet to play for the Toffees this season because of injury, and his current contract with Everton is set to expire at the end of the 2017-18 term.
As a result, he could be available relatively cheaply. There is little chance, unless Barkley pens a new deal, that Everton will be able to get anywhere near the £50 million price tag they originally placed on him, per BBC Sport.
If they are to make any money from Barkley, Everton are likely going to have to sell him in the upcoming January transfer window or else he could go for free in the summer.
It will benefit the Merseyside outfit if both Chelsea and Tottenham try to sign him as the west London side are said to be unprepared to concede defeat in their pursuit of him, per Barlow.
But it could be a big risk from Chelsea to splash out on Barkley. He has long boasted huge potential and intermittently starred on the big stage.
Barkley's inconsistency is a concern, though, as it is no longer legitimate to blame his varying form on youth.
At 24, the England international should now be reaching his peak.
His last two seasons in the Premier League have been encouraging—he has returned 13 goals and 16 assists in 74 appearances—but he arguably has yet to hit the kind of form that would earn him a first-team place at Chelsea.
It seems Chelsea are confident in his ability, though, and keen to add him to their squad to bolster their attack in the second half of the 2017-18 season.