Blatter has said he was "sure" that the prospect of other Gulf nations staging matches, such as Iran and the United Arab Emirates, would be considered by FIFA "at a certain time".
The 77-year-old Swiss also revealed his preference for the 2022 finals to be moved to November and December rather than earlier in the year.
FIFA's executive committee last month agreed to begin a consultation process which will look at all the impacts of moving the tournament from June/July due to the extreme heat in the Gulf at that time of year.
Speaking in the UAE before Friday night's Under-17 World Cup final, Blatter revealed the possibility of matches being played out of Qatar, saying: "I keep a big question mark on this.
"I have just passed through Iran and, even on a political level, people told me they would be happy to host some of the matches.
"So not even in the Gulf state but in the Middle East in general people care about this.
"The UAE would also be very eager, but let's go step by step.
"The first step is to see how it can be played in November and December and this shall be until the next World Cup: we have six, nine, months' time to do so."
Blatter is due to travel to Doha this weekend to meet the new Emir of Qatar and discuss the country's moves to improve working conditions after an investigation revealed dozens of Nepalese workers have died in Qatar this year.
Qatar's supreme committee has written to FIFA outlining its commitment to tackle the abuses.
"I want to avoid all of this criticism concerning workers' rights, but this is another problem," Blatter said, in quotes reported in various newspapers.
"To have the finals in different countries is not a new fact and I am sure it is something on the table at a certain time."