Reports in Spain suggested Bayern coach Pep Guardiola was keen to bring the Barcelona star to the Allianz Arena, and that the European champions were ready to meet his release clause.
However, Rummenigge denied those claims and expects the 26-year-old to stay at Camp Nou for the rest of his career.
"Messi? We are talking about figures here that are simply absurd, a transfer fee that is even higher than what we spent on Javi Martinez. We won't go there," Rummenigge told Sky90.
"Plus I know Sandro Rosell (Barcelona president). Barcelona would never sell Messi. He is a saint at Barcelona and they will not sell him.
"And I think it would be in Messi's best interest to stay at Barcelona. He fits in perfectly there."
Messi's contract with the Liga champions runs until 2018 and he has a €250 million release clause.
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