Messi, who played under Bayern boss Pep Guardiola when the Spaniard was at the Nou Camp helm, has had an underwhelming run of form by his own high standards. He has not scored in his last five league games for the club.
"I know they would never sell Messi. He is a saint at Barcelona," said Rummenigge.
"I think it would be in Messi's best interest to stay at Barcelona. He fits in perfectly there."
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