A source close to French UEFA president told AFP that "an announcement will be made before the end of the week", while another source confirmed that Platini has decided to run.
When asked, Platini's spokesman refused to comment.
Outgoing president Blatter announced last week that the election for his successor would be held on February 26, 2016.
Platini has positioned himself as one of the most outspoken opponents to Blatter's regime, and publicly called for him to stand down after seven FIFA Executive Committee members were arrested on corruption allegations in raids in Switzerland prior to May's election.
Platini, 60, has since emerged as one of the most likely names to run in the election and has the verbal support of four of the six confederations that make up FIFA, with the strongly pro-Blatter Confederation of African Football and that of Oceania the only exceptions.
The former Juventus and France star eventually decided not to run in May's election, having apparently seriously considered doing so at one point, so if he does come forward this time it would indicate a confidence on his part that he can win.
Former Brazil star Zico lacks any experience of international football administration while Liberian FA chief Musa Bility is unknown outside of Africa and Diego Maradona, who has declared an interest in standing, is unlikely to be a serious contender.
Jordanian Prince Ali, who took on Blatter in May's vote, got much of his support from UEFA members and so would be likely to give his backing to Platini rather than stand against him.
Candidates have until October 26 -- exactly four months before the vote -- to come forward. They must have the confirmed backing of at least five of FIFA's 209 member nations, and be cleared by the world governing body's ethics committee, to be able to stand.