The Red Devils have been linked with a host of top keepers after current understudy Ben Foster failed to persuade onlookers that he was the right man to succeed 39-year-old Edwin Van der Sar during the Dutchman's absence earlier in the season.
Inter Milan shot-stopper Julio Cesar and Schalke goalkeeper Manuel Neuer have both been rumoured to have interested United but now reports in Germany believe 24-year-old Adler could be about to join the Red Devils.
The player is said to have a clause in his contract that allows him to leave should United come in with a bid, while the Germany international was a spectator at Anfield last weekend for the 2-0 defeat to Liverpool.
Leverkusen general manager Rudi Voller insisted that Adler's trip to the North West was purely coincidently and refused to reveal if his goalkeeper was heading to England.
"I am delighted to see players being so much involved with their job they travel long distances to witness other matches," he told the Rheinische Post.
"I am happy to see Rene being linked to big clubs right now, this is the best signal we have that we have a very good player on our hands and not so much wrong when setting up our squad."