The midfielder is yet to feature for Everton this season but is believed to be back to full fitness.
The midfielder was close to moving to Stamford Bridge on transfer deadline day in the summer, but a move broke down in the final hours, with speculation at the time that he changed his mind during the medical.
Everton manager Sam Allardyce admitted on Thursday that he was expecting to receive bids for Barkley before the close of the January window. After turning down his contract extension, Barkley's transfer saga is about to reach conclusion this season.
They will look to maximise the price of their homegrown talent, who joined the academy as an 11-year-old and has made more than 150 first-team appearances, but £15m seems to be a generous offer for a player they could lose for nothing in a few months.
Barkley, capped 22 times by England, has previously expressed a desire to play Champions League football and will be eligible to play for Chelsea in their last-16 clash against Barcelona in February.
Chelsea is racing to rush through a deal for Everton star Ross Barkley so that they can ensure that Tottenham doesn't beat them there first. 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.
Barkley, 24, has not featured for Everton this season as he recovers from a long-term hamstring injury, but the Merseyside club began to plan for life without him last summer by signing Wayne Rooney, Gylfi Sigurdsson and Davy Klaassen.