In an interview with Switzerland's Schweizer Illustrierte magazine Blatter also said neutral venues might be better suited for high-profile playoff matches.
Blatter's comments follow last Wednesday's World Cup playoff in Istanbul between Turkey and Switzerland which began with Turkish fans whistling over the Swiss national anthem and ended with a brawl in the players' tunnel.
The Turkish team had earlier complained about Swiss fans whistling over their national anthem during the first leg of the playoff in Bern.
"I consider this whistling to be extremely disrespectful and of course disparaging to national pride Blatter told the magazine.
"I am asking myself whether it even makes sense to play the national anthems. We will at least consider (not playing them).
"We could also insist that the teams shake hands after the match. We cannot have the situation where the winning team is unable to celebrate but must instead sprint off the pitch like thieves."
FIFA spokesman Andreas Herren told Reuters on Tuesday that Blatter's comments were personal suggestions and no formal discussions about national anthems had yet been scheduled.
Herren added that any such proposals would probably not be considered until after FIFA's disciplinary committee delivers its verdict on the events in Istanbul.
Although Blatter said last week the committee would be reporting back before the World Cup draw on Dec. 9 FIFA now says that is unlikely.
"There are a high number of people to be questioned about what happened in Istanbul something like 30 people in all Herren said.
"The investigation will probably not be completed by Dec. 9 because it will require a lot of time and resources.""