Bundesliga - Schalke confirm United Neuer interest
The 24-year-old, who has also been a target for Bayern Munich, has a contract until 2012 with last season's Bundesliga runners-up.
"An international agent contacted me and expressed Manchester United's interest in Neuer," Toennies told Bild newspaper.
"If and when there is a written request from Manchester then we will deal with it."
Schalke coach Felix Magath has said that Neuer will see out his contract but the cash-strapped club may decide to cash in on a hefty transfer fee at the end of this season rather than see him leave as a free agent a year later.
Neuer is Schalke's captain and the undisputed Germany number one.
United could be looking for a replacement for 40-year-old Dutch keeper Edwin van der Sar who will be retiring at the end of the season.