Sheringham was 40 years and 270 days old when he last featured in the top flight, playing for West Ham in December 2006.
Giggs, who recently penned a one-year extension at Old Trafford, would not break the record unless he continues into the 2014-15 season but the former Tottenham man is certain the Welshman can eclipse him.
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"I think he would have to play another season on top of next year [to beat my record]. You have to be that build – I didn't carry a lot of fat when I was playing and he definitely doesn't. He's kept himself in good shape."
With the retirement of Sir Alex Ferguson, Sheringham believes the senior members of United's squad – including Giggs and Paul Scholes, who retired last season but is likely to stay on as a coach – will be vital for the champions as they usher in a new era under David Moyes.
"Without a doubt, they are the ones that lead by example and show the youngsters how it is done," he added.
"People are still looking up to the likes of Giggsy, Scholesy and Rio [Ferdinand] from the next generation."