Neuer has long been the top name on United's list of targets to succeed Edwin van der Sar, but Sir Alex Ferguson feared he was bound for Bayern Munich.
He could yet fill the gap left by Van der Sar's impending retirement, though, after Schalke chief Clemens Tonnies said: 'I have been informed by an international consultant that United are interested in signing Manuel.
Top target: United will be granted permission to speak to Manuel Neuer if they lodge an official bid, say Schalke
'Provided they submit a written offer, we will deal with the matter and give them permission to speak to him.'
The 24-year old has 18 months left on his current contract, and though Schalke are still trying to persuade him to sign a new one, they are resigned to losing him, after struggling to challenge for a European place in the Bundesliga.
Neuer is ambitious about playing at a higher level and looked to be heading for Bayern Munich at the end of the season after Louis Van Gaal expressed an interest in him and was privately assured an approach would be welcomed by the Germany number one.
Calling it quits: United must find a replacement at the end of the season for retiring No 1 Edwin van der Sar
But, in a surprise move by Tonnies, United have at least been given the chance to state their case and attempt to talk the Schalke favourite into uprooting from his home town and testing himself in the Barclays Premier League.
The opportunity will be welcomed by United manager Sir Alex Ferguson, who has already signed Anders Lindegaard but wants at least one more proven keeper, in readiness for van der Sar's departure at the end of the season.
United have also been linked with Julio Cesar, Pepe Reina, Maarten Stekelenburg, Rene Adler and Hugo Lloris, but Neuer has consistently been under closest review.
Reds rage! Fergie fumes as Chelsea defender Luiz escapes red for Rooney foul Fergie to turn to Brown after dismissal rules Vidic out of Liverpool clashManchester United set to land winger dubbed 'the next David Beckham'Giggs in pictures: Sportsmail looks back on his 20-year spell at Man UnitedAll the latest Manchester United news, features and opinion
Explore more:People: Alex Ferguson, Pepe Reina, Louis Van Gaal, Edwin Van Der Sar Places: Munich, Germany