Former Bayern chief exec Rummenigge has declared he'd like to see them sign the Bayer Leverkusen star.
Rummenigge dubbed the Germany international as the best player in the country, a claim that has upset Matthaus.
He told Sky Deutschland: "Bayern Munich recently extended (Jamal) Musiala's contract for around €175 million, which is obviously a lot of money. Saying that someone like that is not the best player in Germany is a slap in the face to Musiala.
"You can say you want to sign Wirtz because he is also a very good player, or as good as Musiala or different from Musiala, but also important for the team. But in this form, I think Kalle has gone off the rails a bit."
He continued: "Why did he speak like that? I don't know, I have no idea and (sports director) Max Eberl won't be happy about it either because he has to sort it out in his daily work. I don't know Kalle at all in that way to explain. I was surprised myself when I read it. But I think Kalle will sort things out sooner or later with his own style, especially internally."