Chelsea appeared close to signing Barkley back in the summer, only for the midfielder to stay at Everton.
The England international reportedly pulled out of a deal before he had his medical.
Since then, Tottenham and Manchester United have emerged as potential suitors with respective bosses Mauricio Pochettino and Jose Mourinho admirers.
But the Daily Mail say Chelsea are confident of landing Barkley from Everton for just £15million.
Speaking today, Toffees boss Sam Allardyce appeared to accept the 24-year-old would quit Goodison Park.
“The club was resigned before I got here that they were going to lose Ross,” he said.
“I can’t see that changing.
“There has still been no contact but I would expect one of the big clubs to come in for him in the next few weeks.”
And the Daily Mail say Chelsea appear likely to succeed where they failed in the summer.
They also add the Blues have enquired about West Ham’s Andy Carroll.
Carroll has found himself out of favour at the London Stadium since David Moyes replaced Slaven Bilic.
And speaking recently he expressed his frustrations at not being a regular.
“It’s been very frustrating,” he admitted.
“I’ve been sitting on the bench – it’s been tough. I’ve been wanting to play.
“I’ve been wanting to get there and start. It’s hard when you’re coming on for the last 20 minutes.”
“I don’t want to be an impact player coming off the bench.”