United tried in vain to sign Sneijder 12 months ago.
"I think they will, without a doubt," Sheringham said. "The manager tried to sign Sneijder last year and when he likes someone he very rarely lets go of that bone and he will go back in for them.
"He did the same for a lot of players – like Ruud Van Nistelrooy. He had a broken leg when he first went in for him but he went back in for him a year later – it wouldn’t surprise me if he goes back in for Sneijder and he finally gets his man."