Sheringham believes someone like Rice will help the club retain possession and compared him to other United greats like Roy Keane and Michael Carrick.
While speaking at the Maurice Newman’s annual charity Golf Day, Sheringham said (via the Manchester Evening News):
"We couldn’t retain possession when it was tough against the Italians - and he was one player who did retain possession. He moved like a Rolls-Royce with the ball out of a problem and then found a pass after that. It’s invaluable to be able to do that and he showed what a top player he is. He’s a top player so he will be going somewhere quite soon.
“He’ll definitely be on Manchester United’s radar. He’s in the mould of Roy Keane and Michael Carrick, who were two top, top players, which you’ve got to have in midfield for Manchester United. So he’d easily fit in there.”
Sheringham believes Rice was amazing at Euro 2020 but was disappointed to see him get subbed off in the final.
“[He’s a player I see at a club like Manchester United] without a doubt. I thought Declan Rice was our outstanding player at Euro 2020. I was very disappointed when he got brought off in the final, it was the wrong decision."
Manchester United need a central midfielder to mount a serious title charge
Manchester United have had one of their most fruitful transfer windows in recent history this summer. The Red Devils signed the likes of Jadon Sancho, Raphael Varane and Cristiano Ronaldo to bolster their squad.
Manchester United have addressed all of their concerns apart from buying a new central midfielder. Many believe Ole Gunnar Solskjaer's side still lack a quality central midfielder who can dictate play from the middle.
The current United squad has some pretty underwhelming players who can play in that number 6 role. The likes of Nemanja Matic and Fred are not consistent enough to be regular starters for the Red Devils at the heart of their midfield.
However, signing Declan Rice from West Ham will be a difficult prospect for Manchester United for a couple of reasons. Firstly, the Hammers have put a £100 asking price for their star midfielder. Secondly, United could face some serious competition from Chelsea in order to land Rice.