The former-Ipswich and Sunderland manager was expected to sign a deal with the newly promoted side, and flew to Istanbul for talks with the club.
But it is thought the ex-Manchester United midfielder is reluctant to relocate his family to Turkey.
On Monday, Kasimpasa's vice president Hasan Hilmi Oksuz revealed the club had reached an agreement with the Irish international, and were looking forward to working with the 41-year-old.
But talks evidently did not go to plan. Keane has also been linked with the vacant Blackburn manager role following Steve Kean's resignation, and his rejection of Kasimpasa is likely to fuel rumours that he could be set to take over at Ewood Park.
But reports indicate there has been no word from Blackburn owners Venkys on whether Keane is on the shortlist for the job.
The former-Manchester United midfielder has been out of a job since being fired from Championship side Ipswich last year.
The ex-Old Trafford enforcer successfully guided Sunderland to promotion in 2007, and kept them in the division before resigning in December 2008. Keane won seven Premier League titles at Manchester United, many of them as captain, and is one of the club's most decorated players.