The Inter Milan playmaker, who has long been linked with a move to Old Trafford, is expected to leave the San Siro at the end of the season.
"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," Sheringham told reporters.
"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."
Sneijder joined the Nerazzuri in 2009 following a two-year spell at Real Madrid.