Wirtz left Bayer Leverkusen for Liverpool after Bayern had previously been in contact with the Germany international and his family.
Asked about the possibility of Bayern pursuing the midfielder again in the future, Rummenigge said recruitment decisions were a matter for the club’s board.
“First of all, that is not my job. It is a matter for the board,” he said.
Rummenigge also pointed to Bayern Munich’s existing options in attacking midfield, including Jamal Musiala and Serge Gnabry, as well as other players who can operate in that area.
“We must not forget that Jamal Musiala and Serge Gnabry play in that position, and there are also other options, such as Ismael Saibari,” he said.
“There is no need to spend the kind of money that Wirtz would probably cost to sign a fourth player for that position.”
Rummenigge did not completely rule out Bayern returning for Wirtz at a later date, however, and said any potential move would depend partly on the midfielder’s situation at Liverpool.
“Could something be possible at some point? I don't know,” he said.
“The question is whether Wirtz is happy at Liverpool. I can't judge that.”
Rummenigge revealed that Bayern had previously maintained contact with Wirtz’s parents before the player eventually chose a different path.
“We were in contact with his father and mother for some time. Then they decided to take a different path, and we respected that,” he said.
Wirtz’s move to Liverpool also surprised Rummenigge, who suggested that the role offered by then-manager Arne Slot had influenced the decision.
“To be honest, yes,” Rummenigge said when asked if Wirtz’s arrival at Liverpool had surprised him.
“We got the impression that he chose Liverpool because the coach at the time, Arne Slot, had promised him the number 10 position, the role he had also had at Leverkusen. That was an important factor in his decision to join Liverpool.”
Rummenigge also said there had not been a major financial difference between the options available to Wirtz.
“There were no big financial differences. He made his decision, and we accepted it,” he said.
For now, Bayern have alternatives in Wirtz’s position, while Rummenigge has made clear that a future move cannot be completely excluded.