The Daily Mail says Schalke are offering to more than double Neuer's wages in an attempt to keep him out of Manchester United's hands.
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.
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.
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 Munich remain uncertain about making a move for Neuer.