Former United striker Sheringham was 40 years and 261 days old when he made his final top-flight appearance - with West Ham in 2006.
But Irwin told the Daily Star Sunday: "I have no doubt he's going to beat Sheringham. Who's to say Ryan won't get another deal at United?
"He's amazing the way he just keeps going on and on and on.
"He leads by example with how he trains, how he never shirks anything and the amount of effort he always puts in every day, every week, every game. It's absolutely remarkable."