Sheringham was 31 when Sir Alex Ferguson bought him, two years older than Van Persie, and enjoyed five memorable years at Old Trafford.
"The manager told me a couple of times he signed me because he looked at my Dad, and he didn't have any extra weight, so he thought I'd be OK for a few years," revealed Sheringham to the Mail on Sunday.
"Van Persie should be coming into his peak. He has had a lot of injuries in the past but 29 is a perfect age for a striker. He doesn't rely on his pace, he has a good knowledge of when to run, when to shoot, when to hold the ball up. Rooney is not far from being in his prime. He's a different build. It will be interesting to follow his situation and see if he fills out."