Sir Alex Ferguson is keen on the 24-year-old after revealing that Denmark No 1 Anders Lindegaard is unlikely to be the only arrival if Edwin van der Sar retires as expected at the end of the season.
In demand: United and Bayern are interested in Manuel Neuer
But Neuer also has huge admirers at Bayern Munich and conspiracy theorists in Gelsenkirchen fear he could be drawn to the Bundesliga champions because his girlfriend Kathy is from the Bavarian capital.
Is that the way out? Schalke could struggle to keep hold of Neuer
Neuer showed his quality by helping Schalke to a 2-0 win against Bayern on Saturday but, as another supposed clue to his future, he then refusedto join a team-mate in singing the lyrics of a song by punk band Die Toten Hosen: 'many things can happen, many things can occur, I just knowone thing for sure, I'd never join FC Bayern Munich.'
Nonetheless, under-pressure Bayern boss Louis van Gaal is understood to be cool on having a deal for Neuer forced on him by bosses and Schalke insist they are under no pressure to sell.
'A year ago, we would maybe have had to think about a transfer in the situation we were in, but not now,' said coach Felix Magath. 'We are nowfar better off financially and do not have to sell Manuel Neuer at all.'
How long Neuer will be happy to stick around at an under-performing club, however, remains to be seen.
Magath optimistically hopes the weekend win will turn Schalke's season, but they sit fourth from bottom in the Bundesliga after last year's high of finishing second and qualifying for the Champions League.
EXCLUSIVE: Fergie eyes Germany 'keeper Neuer for his new No 1Fergie admits Van der Sar is retiring - and paves way for £15m De Gea bidMan United on brink of £3.5m deal to sign Denmark goalkeeper LindegaardDe Gea on brink of £15m United move as Sir Alex plans for life without Edwin
Explore more:People: Alex Ferguson, Felix Magath, Louis Van Gaal, Edwin Van Der Sar Places: Manchester, Munich, Germany