The 34-year-old has yet to come face-to-face with the Red Devils since leaving for Real Madrid in 2003, and is not assured a starting place in the last 16 first-leg having been benched in recent weeks.
The ex-England captain - who made more than 350 appearances for United - has vowed not to celebrate should he score against Sir Alex Ferguson's side, and insisted that he is not looking for revenge on what he says will be two emotional nights in Italy and back at Old Trafford on March 10.
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However, Sheringham - who won the treble with Beckham in 1999, scoring in the Champions League final against Bayern Munich - believes the LA Galaxy loanee will quietly be keen on avenging his sale by Ferguson, who had grown increasingly frustrated by the midfielder's celebrity status
"Does he have a point to prove? Without a doubt. He will want to do really well to let Sir Alex know what he did by letting him go," he said in the Mail.
"He will want to put on his best performance. He will be itching to play, particularly at Old Trafford in the second leg."
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