In comments widely reported in British media, Michel Platini said there was no reason why matches for the 2022 tournament could not be held across several countries surrounding Qatar.
"I hope it will be a World Cup of the Gulf," Platini was quoted as saying in several reports.
FIFA's decision to award the World Cup to Qatar -- a tiny oil-rich nation where temperatures in summer regularly soar past 43 degrees -- has attracted a firestorm of controversy.
FIFA President Sepp Blatter has already said he "expects" the tournament to be moved to the cooler winter months and told L'Equipe last month in an interview that neighbouring Gulf countries could also host games in 2022.
Now Platini has voiced his support for the idea, saying that "it could be the World Cup of Qatar but played in the Gulf".
"I think we need political people (for this to happen), but I think so," Platini was quoted as saying.
Asked why co-hosting the tournament could be considered when it was never mentioned during the bidding campaign, Platini was quoted as saying: "Who will remember the words in 12 years? In 12 years everybody will be happy to have a very well-organised World Cup and not remember what's happened before.
"When I organised the World Cup in France we did (things) differently from what we proposed in the bid."