Blatter pledged in 2011 that this term would be his last in charge of world football's governing body.
But the 77-year-old appears set to go back on his promise after admitting to Swiss radio station RTS that he would like to stay on in the job.
"If I have the health – and I am currently in good health – I don't see why I would stop the work. A work which continues," Blatter said.
"FIFA needs consolidation. Many people say it needs to be continued.
"I will not shout 'I'm candidate' but if the members associations ask it to me, then I will not say no."
FIFA's leadership will be taken to a poll in May 2015, a time when Blatter, who has been in charge since 1998, would be 79.
Blatter's interest in the position could see him come up against former colleague Jerome Champagne in the race.
The Frenchman, who used to be FIFA deputy secretary general, announced his desire to run for presidency in January.
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