The 23-year-old German international, who has made more than 100 Bundesliga appearances for Die Königsblauen, has become one of the most sought-after glove-men in Europe, with Bayern Munich previously expressing an interest in his services.
According to reports, Neuer is one of a string of shot-stoppers - including CSKA Moscow stopper Igor Akinfeev and Lazio custodian Fernando Muslera - wanted by the Red Devils as a future replacement for ageing Dutchman Edwin van der Sar.
And Neuer has confessed that he is delighted with the Old Trafford outfit's apparent admiration for him.
"I really want to play Champions League football next season. We're all thinking about our careers and so am I. Hopefully Schalke manages to qualify for the Champions League," he said in Sport Bild.
"I know that Manchester United are keeping tabs on me. They've sent scouts to several Schalke games and they watched me in action with Germany U21s against England last summer.
"I am absolutely flattered that a big team such as Manchester are interested in me. That shows that I'm on the right track and that I haven't made too many mistakes."
And Schalke defender Marcelo Bordon has revealed that he believes the club should cash in on Neuer's services now while his reputation and value is sky-high.
"It would be a huge blow for the fans if Schalke sold Manuel. However, one should not forget what would be best for the club," he said.
"Schalke's financial situation is very important, too. It could be better for the club to cash in on Neuer. The club could get a lot of money for a talented goalkeeper such as Manuel."
