Cole has been considered England's first-choice left-back for a number of years now, but Baines's recent form has led many to call for his inclusion in the England starting XI.
However, Baines believes that Cole's participation in Europe's premier competition gives the Chelsea man an advantage.
"I wouldn't have thought I'm on an even keel with Ashley because he's with a club that's playing at the very top level," Baines said in The Sun.
"I'm sure playing in the Champions League carries some weight because you are up against the best players in the world.
"So it's no small task trying to get into the team ahead of Ashley."
Baines has made 13 appearances for England, including starting five of their last six matches.