Robert Lewandowski scored two goals against Barcelona in the Champions League group stage in 2021-22
Barca president Joan Laporta said he was hoping for a "positive response" from the German champions.
Lewandowski, 33, has been at Bayern since 2014 but said in May his "story is over" at the club.
"We have made an offer for the player, we are waiting for the response, we will see if it is positive," Laporta said on Thursday.
Lewandowski has one year left on his contract.
Laporta would not discuss specific details about Barca's offer but it has been reported they have offered £33.8m plus a £4.2m bonus for the player.
Barcelona have dismissed rumours that Bayern, suspicious of Barca's economic situation, wanted payment for the transfer of Lewandowski up front.
"I don't believe it," added Laporta. "I believe it's information from a cat and it was a joke. It doesn't come from Bayern.
"We made an offer and they must now weigh it up."
Lewandowski has scored 238 league goals in 252 appearances over eight years for Bayern, winning eight Bundesliga titles and the Champions League with the club.
-- Courtesy of BBC Sport