The Croatian striker has been heavily linked with a move to the Premier League, after a number of fall outs with Pep Guardiola this season.
The European Champions have already confirmed the signing of Robert Lewandowski from Borussia Dortmund at the end of the season, but now it seems they want to keep Mandzukic as well.
His current contract at the Allianz Arena runs until 2016, and Bayern chairman Karl-Heinz Rummenigge hopes the centre forward will stay put.
“I am definitely aware that many clubs have started to show an interest in Mario’s services, but I believe he will be with our club way beyond the end of this season.”
The news will come as a bitter blow to both Arsenal and Chelsea, who both consider themselves in desperate need of a world class striker.
Nicklas Bendtner is set to leave Arsenal at the end of the season after his latest controversy in Copenhagen, whilst Jose Mourinho is keen to offload all three of his strikers in the summer after a season that has seen them all mostly misfire in front of goal.