The Frenchman has opted to continue to focus on his Uefa duties, with his contemporaries hopeful his decision will ensure there is "no battle" between the two governing bodies
The former France international was believed to be considering running for the job of president of world football's governing body, but he stated at a meeting of 54 European football associations in Monte Carlo on Thursday that he will stay on in his current position instead.
Fifa executive committee member Michel D'Hooghe was quoted as saying by the BBC: "It was a very positive message - he said he would like to continue as Uefa president and I am pleased that it means that this time there will be no battle between Fifa and Uefa."
Platini has heavily criticised Blatter on more than one occasion and stated earlier this year that the 78-year-old was "finished" as the right man to lead Fifa.
The Swiss had previously stated that he would step down at the end of his fourth term but later reneged on the decision and made it clear he will stand for election again.
Blatter has been working at Fifa since 1975 and was first elected as the governing body's president in 1998.
Irrespective of Platini's announcement, Fifa's former general secretary will not be unopposed for next year's elections, as former French diplomat Jerome Champagne announced earlier this year that he will challenge Blatter.