Bayern were confident they had finally found a solution to the contract stand-off after presenting him with a one-year deal that would automatically kick in for a further 12 months, if he made at least 20 appearances next season.
But a collapse in the negotiations has opened the door for the Toffees boss David Moyes to swoop for the 32-year-old German international.
One of Moyes boys? Klose is being eyed by the Everton boss
A statement released by the club confirmed Klose's departure: 'Negotiations led to no agreement and Klose's contract running out on June 30, 2011 will not be extended.'
Moyes knows transfer funds are strictly limited, following a meeting with chairman Bill Kenwright. But he now knows he only needs to come up with an acceptable wage package to have a chance of landing one of German football's most prolific scorers.
On leaving the club the striker said: 'I had four very good and successful years in Munich and I want to thank Bayern. Playing for this club was something special.'
Do the figures stack up? Moyes can put a generous pay package together
Klose won the Golden Boot at the 2006 World Cup after notching five goals in the finals for the second successive time. His overall tally of 14 goals at World Cup tournaments leaves him just one behind Brazil's Ronaldo as the all-time record scorer.The German international scored 24 goals in 98 league games for Bayern since joining in 2007, has also been linked with a possible move to Spain.
International quality: Klose has a prolific record for Germany at the World Cup
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