Giggs penned a one-year contract extension in March which will see the former Wales international continue playing into his 40s.
However, the midfielder – who has won 13 top-flight titles – would need to play in the 2014-15 campaign to have a chance of beating Sheringham’s record.
But the former Tottenham Hotspur forward reckons Giggs is fit enough to continue playing for another two seasons and could emulate his feat.
“I hold the record for an outfield player,” Sheringham told United’s website. “But Giggsy has still got a couple of years left in him.
“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.”
Sheringham also believes Giggs and Rio Ferdinand, plus the recently retired Paul Scholes, can continue to inspire the next generation and ensure United keep progressing.
“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.”
ENHANCED ODDS: Get 10/1 on England to beat Italy