Barkley was said to be on the verge of joining the champions in the previous transfer window, but opted against a move on Deadline Day.
The England worldwide has now returned to training after a painstaking rehabilitation and Antonio Conte, the Chelsea head coach, wants to bolster his squad in January.
Barkley has been at Everton since he was 11-years-old, having been spotted by the club's late and prolific former scout Sid Benson, and made 150 Premier League appearances.
Chelsea head coach Antonio Conte has been vocal in recent weeks about his desire to see the club strengthen his squad "in the numerical aspect" during the January transfer window, and the Blues are expected to actively explore other deals throughout the month.
Chelsea, though, are prepared to pay to take Barkley immediately and Sam Allardyce on Thursday admitted that Everton remained resigned to losing him.
It looks like it's going to happen. Rather than seeing Barkley leaving Goodison for free at the end of the season, accepting a deal around 15 million is indeed a better option for Everton.
The England midfielder, who have just six months left of his current Toffees deal though he's not featured for Everton all season, recently returned to training with the first team and has played in a behind closed doors friendly.