Barkley was hot property during the summer transfer window after refusing to sign a new contract at Goodison Park with Chelsea and Tottenham just two of the clubs to show a keen interest.
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.
And now, barring late hitches, he is likely to secure a move to Chelsea.
Barkley, capped 22 times by England, has previously expressed a desire to play Champions League football and would be eligible to play for Chelsea in their last-16 clash against Barcelona in February if he completes a move to the club.
With both Tottenham and even Arsenal interested in the England playmaker, the Blues want a swift resolution to the transfer rather than spend the entire January window.
Per Paul Joyce of The Times, the Everton midfielder - whose contract expires this summer - is on his way to Chelsea to undergo physical tests before putting pen to paper.
And the bookies claim a deal is getting ever nearer as the 24-year-old is now 1/5 odds-on to leave the Toffees.
Barkley has not featured for Everton this season as he recovers from a torn hamstring.