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The England international has missed the whole of the season so far through injury.
But Barkley is edging close to a comeback from his hamstring issue.
It is said the 24-year-old is two weeks away from fitness, just ahead of the January transfer window.
Tottenham remain interested too, with Barkley seeking game time away from Goodison Park.
New Everton manager Sam Allardyce still faces losing the midfielder, with his contract expiring next summer.
And with no new deal forthcoming, the Daily Mail claim Chelsea are preparing another bid.
Ross Barkley: Chelsea fans livid as Everton midfielder rejects Blues transfer
“Chelsea will look to discover what it might take for Everton’s No.8 to become interested”
The Blues want to lure Barkley to Stamford Bridge and are ready to make contact again.
Chelsea will look to discover what it might take for Everton’s No.8 to become interested in joining.
Antonio Conte’s side are plotting to bolster the squad in mid-season.
And the Daily Mail add Barkley would help ease the workload on Cesc Fabregas.
The Spaniard has been relied upon for creativity at Chelsea this term.
And Barkley may be granted more opportunities than before too following Conte’s switch towards a five-man midfield.
Chelsea have not conceded defeat yet to London rivals Tottenham.