The Blues have come back in for the 24-year-old after he chose to remain in Merseyside to continue his recovery from a serious hamstring injury, despite advanced talks on transfer deadline day in August.
Barkley has only six months remaining on his contract, which means a reduced price could be agreed between the clubs after Chelsea offered double the amount in the summer.
Tottenham are also interested in Barkley but look like outsiders to complete the deal at this stage with Chelsea making a strong approach, while Everton are resigned to losing their academy product, having been without him all season.
Barkley is close to making his return to the pitch, and he could be lining up in Chelsea's blue. Manager Antonio Conte has revealed that Chelsea are aiming to add more players for their undersized squad because the club are still competing on all four fronts.
"For sure, the club will try to do their best in the market to improve the squad from a numerical aspect," Conte said last week. "I'm a coach, I have to work with my players and my task is on the pitch. The transfer market is for the club and they must decide if they want to improve my squad."
He also added that no player will be sold or sent on loan until the Blues add a replacement. Goal revealed three weeks ago that Charly Musonda will decide on whether he wants a loan move later in the transfer window , and his former club Real Betis are just one team to have registered an interest.
It is often hard for the biggest clubs to secure their best targets in the January transfer window, but Chelsea also have a long-term interest in Juventus left-back Alex Sandro, who has still yet to renew his contract despite ongoing talks.