Neuer has long been reported to be one of the possible replacements for Edwin van der Saar, who will retire at the end of the season.
Tonnies told the Bild newspaper: “An international agent approached me and informed me that Manchester United are interested in Neuer.
“If Manchester United make a written inquiry then we will deal with it.”
Neuer’s current contract with Schalke is set to expire at the end of next season.
