The 36-year-old five-time winner has scored five goals in four European games so far this season, including a double against Atalanta on Tuesday which salvaged a point.
He has also scored late on against the Italians and Villarreal at home and Sheringham, who scored in the famous 1999 Champions League final comeback against Bayern Munich, says United’s aims should match that of their talisman.
Man Utd should be matching Cristiano Ronaldo’s European ambition, says Teddy Sheringham
‘When you’ve got Ronaldo in your team, you’re looking to win it,’ he told Genting Casino.
‘Ronaldo will be looking to win it – he has done it before on many occasions and he will want to win it again.
‘Things change very quickly and all United need to do is get to the next level and after that result [vs Atalanta], United are in a good position to get to the next level..
‘That is why when the chance to sign a player of Ronaldo’s calibre comes up, you have to snap them up.
Ronaldo has scored five goals in four games and has won the Champions League five times
‘For me, he is one of the two best players in the world and has been for the last twelve years – he’s phenomenal.
‘He is deadly, he knows how to score goals, he’s so focused, he’s so professional. He is unbelievable. Where would they be without him? I’m not sure.’
United are joint-top of their group with Villarreal on seven points, with two matches left to play.