By ESPNSTAR.com staff
The Red Devils were heavily linked with a move for the Holland international at the start of the season, with manager Sir Alex Ferguson reportedly identifying him as the ideal replacement for the then-retired Paul Scholes.
However, the move failed to materialise and United's problems in midfield were so bad that Scholes himself offered to come out of retirement, and has since played an integral part in the latter half of their campaign.
With the Barclays Premier League title all but lost to arch-rivals Manchester City now, United look set to reinforce their squad this summer, especially with no word on whether Scholes will play on for another season.
And Sheringham believes Ferguson is not the kind of manager who will miss out on an opportunity to sign a player he wants twice.
"I think they will [make a bid for Sneijder], without a doubt," Sheringham said, according to the Daily Mail.
"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."
It is still possible that the 37-year-old Scholes could play on for another year, but Sheringham reveals he himself had problems maintaining his performance levels when he reached his latter years, even though he only retired at 42.
"Looking back at my career I realised that in the last three or four years, I started the campaign very, very well but I couldn't sustain it over a whole season, and it petered away long before we even reached March," the former England international admitted.
"You only realise after you have retired how much you struggled."
Despite only moving to Old Trafford after he had turned 31, Sheringham enjoyed plenty of success with United and played a key role in the treble-winning season of 1998/99, scoring goals in both the FA Cup and Champions League finals.