The Bayern Munich chairman has insisted that the club has no plans to make a move for the prolific attacker and believes Barcelona would never sell its star player.
A recent report from Spain suggested that Bayern was ready to meet the 26-year-old's 250 million euro exit clause, with the club's honourary president Franz Beckenbauer further fuelling speculation last week with his comments that Messi would be a good signing for the Bundesliga champions.
However, Rummenigge has now made it clear that the Bavarians have no intention of splashing the cash on the prolific attacker.
"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 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."
The attacker has a contract with Barca until June 2018.