The 29-year-old has scored eight goals in 12 appearances in the Premier League for Sir Alex Ferguson's side so far this season, adding three more in the Champions League.
"Robin has made a massive impact since he joined," Cole told The Mirror. "He's carried on for United where he left off with Arsenal last season, scoring bundles of goals.
"I think he's also joined at a good age. People might say it's not a good age, given he's 29 and United paid £24m for him, but I don't think he has anything to prove to anybody.
"Everyone knows what he can do and I think that makes the transition even easier for him, because he's already shown what he can do and the pressure's off."
Cole played for United between 1995 and 2001, winning the Premier League five times and the Champions League once.