While it has been known for some time that the Italian playmaker was set to leave the Munich-based club owing to his rancorous relationship with manager Louis van Gaal, the new revelation shows how desperate Bayern is to get rid of its erstwhile star striker.
However Hoeneß said that despite the urgency, Bayern had yet to receive a firm offer from another club.
“We still don't have any definite offer, even though we are prepared to lend him out at no fee or sell him,” Hoeneß said.
If necessary, they were prepared to demand no transfer fee “because we want to have calm,” Hoeneß said.
“The topic of Toni will certainly preoccupy the media as long as he is here.”
By getting rid of 32-year-old Toni, Bayern would wipe one of its top earners from its payroll.
The striker, who was contracted to the club until 2011, has already talked to clubs in Italy, Spain and England.
Although Toni was the Bundesliga's top scorer in the 2007/08 season, an Achilles tendon injury and a monumental falling out with manager van Gaal have put him on the bench for most of this season.
Hoeneß said the club still had nearly two weeks to firm up a deal.
“Now we're waiting to see what happens,” he said. “The transfer period starts on January 1 and we still have some time before then.”
He said Bayern was well-placed with their forward combination of Ivica Olic, Miroslav Klose und Mario Gomez.
“With these three we have very strong forwards and varition possibilities,” he said.
Hoeneß also brushed aside speculation that manager van Gaal's future of the club had been hanging by a threat.
“The position of Louis van Gaal was never in danger.”