The Germany international is out of favour at Real Madrid, having failed to break up the midfield partnership of Toni Kroos and Luka Modric.
Centre-back Sergio Ramos was even preferred in midfield for the first leg of his side's Champions League semi-final with Juventus last week, with Khedira set to leave when his contract ends in June.
Schalke - who were beaten by Madrid in the last-16 of the competition - are ready to offer him a fresh start, however, but will face competition from a host of clubs for his signature.
"I would prefer us to conduct our business in private," said Heldt. "But it is true that we want Khedira for the coming season. However, we are not the only club who wants him."
The 28-year-old confirmed in March that he would not be extending his stay at the Bernabeu, sparking rumours of a possible move to Manchester United or Arsenal.
Khedira joined Madrid from Stuttgart in 2010 and was a regular under Jose Mourinho, but has failed to make an impression on current boss Carlo Ancelotti.