South Africa Considers Vuvuzela Ban
Some supporters have criticised the lack of traditional atmosphere inside stadia with the horns drowning out chanting and singing.
The drone-like noise is picked up by stadium microphones and has led to complaints from broadcasters, while some players claim they are unable to hear their team-mates during matches.
"If there are grounds to do so, yes," said Jordaan when asked if a ban might be introduced.
He told BBC Radio 5 Live's Sportsweek programme: "We have heard from the broadcasters and other individuals and it is something we are evaluating on an ongoing basis.
"We have tried to get some order with it. We have asked for no vuvuzelas during national anthems or anyone is making an announcement. I know it is a difficult question but we are trying to manage it as best we can.
"This matter has been raised on many occasions and my personal view is that I would prefer singing.
"It has always been a great generator of a wonderful atmosphere in the stadiums and we will try to encourage them to sing because that is the strength.
"It is a huge debate and it will continue, but we did say that if one lands on the pitch in anger then we will not think twice and take action."