A move to the Blues was on the cards in August but the 24-year-old Toffee pulled out at the last minute, scuppering a £35 million transfer.
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.
The same report claimed that Tottenham Hotspur ended their interest in Barkley due to the player's wage demands, putting Chelsea in the front seat for his signature.
But negotiations between the clubs resumed once the transfer window re-opened on 1 January.
The Everton midfielder is out of contract at the end of the season and new manager Sam Allardyce admitted on Thursday that the club is resigned to losing its homegrown talent, who has rejected offers to extend his stay at Goodison Park. "I can't see that changing".
With Antonio Conte frustrated with the Chelsea board, after not getting the targets he wanted including watching Tottenham steal Fernando Llorente on deadline day from under their noses, Romelu Lukaku chose to go to Manchester United instead.
It looks like it's going to happen.
Barkley was out of contract at the end of the season, and could have left Everton on a free transfer.
Barkley opted against leaving Everton while carrying a hamstring injury that has forced him to sit on the sidelines so far this season.