Giggs' form and fitness both looked top-notch during United's 20th title-winning campaign.
"I hold the record for an outfield player," Sheringham told ManUtd.com, "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."