Bayer 04 refused an initial approach from the Bavarian side for the 23-year-old but their interest has not been dampened as they look to strengthen their midfieldhere.
Bayer Leverkusen will only sell Lars Bender to Bayern Munich if they receive an offer of €25 million (£19.6m), according to a report by Bild.
Die Roten made an inquiry over the availability of the holding midfielder earlier this month but their interest was swiftly brushed aside by Leverkusen, who refused to sell the German international.
However, Bayern coach Jupp Heynckes has since admitted that he believes Bender to be an interesting option as his side look to purchase a new midfielder. Club chairman Karl-Heinz Rummenigge has also raised the pressure on their Bundesliga counterparts to sell as they hope to improve upon their three runners-up finishes from last season.
"We could imagine that Lars Bender is on the agenda in Bavaria. Every player has his price. If we are willing to pay this [price], it is conceivable that the player will wear the shirt of Bayern," said Rummenigge.
"We'll see whether Karl Hopfner [financial executive] can keep things hot and can push things forward a bit."
Reportedly, the threshold at which Leverkusen will cave from their refusal to sell stands at the €25m mark, which would be the second-highest Bundesliga transfer fee ever paid.
Leverkusen CEO Wolfgang Holzhauser, however, has not been impressed by Bayern's approach and remains adamant that the club will not part company with the 23-year-old.
"Lars Bender is a cornerstone of our future and we cannot let go of a cornerstone," he said.
Andre Schurrle has also been linked with a move away from Leverkusen and is reportedly unhappy with the club's decision to turn down an identical offer from European champions Chelsea.