The Croatia international has been heavily linked with a move away from the German champions in recent months due to the impending arrival of Borussia Dortmund forward Robert Lewandowski.
Juventus had been mooted as one possible destination, although both Mandzukic and Bayern representatives have sought to deny such reports.
And despite Lewandowski moving to the Allianz Arena at the end of the season, Sammer claims Mandzukic is going nowhere.
The former Germany international said the 27-year-old remains "incredibly important" to Pep Guardiola's side.
"Nobody even has to bother making an approach for Mandzukic," he told Sky90.
"He is incredibly important to Bayern. I always affectionately say that he plays like an animal.
"It is simply amazing how much work he does for the team and how much running he does during a game."
