Cole is out of contract at the end of this season and could even leave the club in January if the right deal is offered to him.
Baines is seen as Cole’s replacement for both Chelsea and England in the coming months and his form this season has made him one of the best full backs in Europe.
Manchester United and PSG are both also after the 28-year-old who is valued at £15million by Everton.
United tried to bring Baines to Old Trafford in the summer but they failed to match the Toffees’ asking price that has increased since then.
David Moyes will not want to lose any of his key players in January no matter what figures are involved, but it is likely that Chelsea, United and PSG will be happy to wait until the summer.