According to The People, Baines and Cole will renew their international rivalry at club level, with Chelsea poised to make a summer move.
It is thought that they also want to tempt David Moyes to Stamford Bridge in the summer and want him to bring his prized asset with him.
The report suggests that Baines will play in an advanced midfield role, before returning to left-back when Cole quits.
Baines has pushed Cole very close for an England starting place in recent months and many predict that he will start ahead of the 32-year-old in the coming internationals.
Manchester United are also said to be interested in the defender, who would command at least a £14m transfer fee.