Coach Ottmar Hitzfeld reconfirmed his departure in the end of the season on Monday, when the Bundesliga joint leaders reassembled after the winter holidays.
Hoeness said the club is in no hurry to find a replacement and urged the media to co-operate.
"We won't leave it until May or June, but it's not our intention to come up with a name in the next two or three weeks either," Hoeness was quoted by the club website as saying in a press conference.
"I don’t have a problem with a proper debate in the papers.
"But I would urgently request the media to desist from half-truths and lies, which would provoke a very sensitive reaction from our side," he added without elaboration.
Hitzfeld was re-signed as Bayern manager in February 2007 to "rebuild the team" and he believes his job would be done by the end of the season.
He is reportedly in talks with the Switzerland to manage their national team following EURO 2008.