According to a report from the Swiss newspaper Schweiz am Sonntag, which cited unnamed sources, Blatter is considering the reversal in course because of support he has received from Africa and Asia.
The reported move by Blatter prompted Domenico Scala, who is in charge of the presidential election, to warn the 79-year-old not to go back on his promise to resign.
"For me, the reforms are the central topic," Scala said in a statement. "That is why I think it is clearly indispensable to follow through with the initiated process of leadership change as it has been announced."
The FIFA executive committee is set to meet July 20 to determine the date of the next election.
This wouldn't be the first time Blatter has said one thing and done another.
In 2011, Blatter announced he would not seek another term as president in 2015. But in 2014, he declared "a mission is never finished and my mission is not finished." Blatter said he would again seek reelection at the next FIFA Congress.
FIFA has seen itself enveloped in a bribery and corruption scandal that has resulted in the indictments of 14 individuals including some top members of the organization and an early-morning raid of a posh Zurich hotel ahead of the congress.
Despite the scandal revelations, Blatter was able to win reelection in May when challenger Prince Ali bin-Hussein withdrew from contention after forcing a second round of voting.
Blatter received 133 votes to Ali's 73 in the first round, which requires a three-fourths majority to win. The second round of voting would have required a simple majority.
The Associated Press contributed to this report
Follow Matt Wilhalme on Twitter @mattwilhalme