Bayern Munich failed to defend the trophy they won last season as Paris Saint Germain held their own to progress on the away goals rule after a 3-3 aggregate scoreline.
Joachim Low will leave his role as Germany manager after this summer’s European championships and Flick has been touted as one of his replacements.
There is friction between Flick and some of the Bayern Munich hierarchy and Tuesday’s elimination from Europe’s Premier club competition at the quarterfinal stage could hasten his departure from the Allianz Arena.
"I already said two weeks ago that in my opinion, this is Hansi Flick's last season," Matthaus told Sky Germany.
"I've said that Hansi Flick is right at the top of the DFB [German Football Federation] list, and then nothing else for a long time. There's an offer from the DFB, yes.
"So, they want Hansi Flick and I think - or rather, I'm convinced - that Hansi Flick will no longer be Bayern coach after this season.
"That means the last game against Augsburg at home will be Hansi Flick's last game as head coach of Bayern."
Flick replaced Niko Kovac as Bayern Munich manager in November 2019 and has won the Champions League, Bundesliga, DFB-Pokal, UEFA Super Cup, FIFA Club World Cup and German Super Cup while in charge of the Bavarians.
