The German club hope to convince the 24-year-old to give them two more years before inevitably moving on to bigger things.
His current £32,000-a-week deal expires in 2012, but Schalke are offering him £80,000 a week to extend for a further year so they can command a substantial fee when they do cash in.
Hands off: German side Schalke are determined to hold on to goalkeeper Neuer
Their current strategy is to scare off suitors with an over-inflated £30million price tag, but Schalke know they will have to negotiate down if Neuer rejects the offer.
Bayern Munich are also very interested but are giving 22-year-old Thomas Kraft a chance to show he can step up.
Sir Alex Ferguson is still in the market for another keeper despite already tying up a Janaury deal for Denmark No 1 Anders Lindegaard.
Current Old Trafford first choice Edwin van der Sar is expected to retire at the end of the season and United could pounce while Bayern remain uncertain about making a move for Neuer.
Bowing out: United veteran Van der Sar
The Barclays Premier League giants are also monitoring Rangers' Allan McGregor and Atletico Madrid's David de Gea among others, while reports in Spain claim they could move for emerging Valencia keeper Vicente Guaita after his impressive performance in the 1-1 Champions League draw at Old Trafford on Tuesday night.
Neuer's agent Thomas Kroth confirmed talks with Schalke were set for the winter break in Germany and coach Felix Magath said: 'Of course we want to keep the best goalkeeper in the world. But I can't say anything about the details. It would be nice if we could start the second half of the season with clarity.'
Money is not the only issue for Neuer, who is enjoying Schalke's progress in the Champions League this season but will wonder when another opportunity comes in the competition.
After a shocking start to the campaign, last season's Bundesliga runners-up sit 15th and just six points off the bottom.
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