The 28-year-old striker, who has been strongly linked with a number of Premier League clubs, revealed that he has already held talks with Bayern.
Speaking from Croatia's World Cup camp, Mandzukic said that he was not happy playing under Pep Guardiola's style of play and that he decided to leave after being left out of the squad for the German Cup final.
"A lot has been written and said about my future, especially before the German cup final in Berlin and I can tell you that before this - I think on May 8 - along with my agent Ivan Cvjetkovic, we had a decent conversation and exchange of views with Karl-Heinz Rummenigge [Bayern chief executive]," he revealed to Jutarnji List.
"I said to him that I had decided to change and that it was fair to inform him and the club's leadership."
Mandzukic admits he was far from happy playing under Guardiola and his approach to management.
"He knows I'm not fond of the constant media appearances and continuously clarifying things in the media," he said.
"I think it is fine that I was frank with the club. Bayern is a fantastic club, and indeed it was not until recently that I thought about going - I never thought it would happen like this, but let's be honest - I do not correspond with the style of game that Guardiola wants to play.
"After the first game with Real Madrid [in the Champions League semi-finals] I definitely realised that no matter what happened I could not be at my best.
"Because of this, I think it is best that we part company.
"I thank the club for offering me a contract extension, and I thank Guardiola who is a great coach and I wish everyone at the club well in future, their fans have always been beautiful with me - but now it's time for a new challenge."
Mandzukic insisted that a decision on where he will go has not been made and he will not look at it until after the World Cup finals.
"When there is concrete news, everyone will be told but I am now concentrating on the World Cup," he added.
Surely Chelsea would want Mandzukic. He can play on his own up front or could be used with a Costa style player with devastating effect. I do understand though that Costa could be considered a very similar player in the way he nicks goals but I could see them working well in helping win games in a defensive system. Its not as if they have many back up strikers that Mourinho trusts when (not if) Mr Costas hamstring gives in next season.. A better plan B than liverpool's (I do love Lambert though). I understand also that is would be rare to see two strikers in Mourinhos system but for set pieces and last minute goals. Mandzukic is a king. 10 assists + 26 goals culminating in a KP+assist average of 2.64 a game. I'm pretty sure there aren't that many people in Europe that can touch that. To wrap up.....Chelsea buy him....- danliverpool