The Sunday Express says United have earmarked Baines as the eventual replacement for French international left-back Patrice Evra but he won't come cheap.
Baines, 28, says there's more to come from him.
He said: "There's not one person out there who doesn't have something to improve on. I am as conscious of my weaknesses, as anyone is, because I live with them. I know what they are and I am always working on them and trying to do things to make sure they don't get exposed."