Klaus Stöhlker, who acted as Mr Blatter’s official adviser during the recent election campaign, said he is actively considering reversing his promise to stand down.
His comments come two weeks after Mr Blatter dramatically announced he would resign.
In a statement FIFA said: “Klaus Stöhlker’s mandate from the FIFA President ended on 31 May 2015. The FIFA President would like to point to his remarks from 2 June.”
In his resignation speech on that day Mr Blatter said he was going because he did not feel he had the support of the entire football world, and that he would not be a candidate in the emergency election.
Mr Stöhlker, a public relations adviser based in Zurich who stressed he is not an official spokesman, said Mr Blatter has received messages of support from Asia and Africa, and is currently deciding whether to remain in post.
He said: “At the moment there is not a convincing candidate to replace Mr Blatter with the same level of qualifications, of languages, of contacts, and knowledge of football.
“As long as there is not such a candidate it remains open for Sepp Blatter to run again.
“There are some people that are asking him not to stand for the next election, there are some people that are asking him not to resign