The veteran Germany international is likely to leave the Gunners at the end of the season after losing his place to Manuel Almunia.
Reports had claimed Bayern could sign Lehmann to replace Oliver Kahn, who is retiring from football at the end of the campaign.
But the German giants' general manager Uli Hoeness says Michael Rensing will be given the chance to be Kahn's long-term successor next term.
"We have promised Michael over and over again that he would be our first choice when Oliver Kahn retires," Hoeness told German television channel DSF.
"It would be relatively senseless to replace one 38-year-old with another, besides Lehmann is not the sort of player to sit on the bench waiting for Michael to get ill or injured."
Bayern president Franz Beckenbauer also acknowledged it would be unlikely that Lehmann would pitch up at the Allianz Arena.
Beckenbauer told Bild: "I would exclude anything, but I can't see how Lehmann would come to Bayern, especially as there is still some animosity from earlier times."