Jordaan told the BBC in an interview that he had to consider the option of banning the trumpets.
"If there are grounds to do so, yes," he said.
Fifa president Sepp Blatter supports the trumpets.
"I have always said that Africa has a different rhythm, a different sound," he said in a Twitter update.
"Would you want to see a ban on the fan traditions in your country?"
But while the ear-splitting plastic trumpets might end up muted in the BBCs screenings, their drone is gaining popularity outside the stadiums of South Africa, and they are predicted to be a common sound at sporting events across the world.
The horns sold out in supermarkets across the UK and virtual vuvuzela apps are soaring on the Apple iTunes charts.
During England's game against America on the weekend the horns were blasted in English pubs and constant shipments have been ordered from South Africa.
Supermarket chain Sainsbury's sold one "Vu Vu" horn every two seconds on Saturday- shifting 22,000 of the instruments in 12 hours before England's game.
It expects to sell out of its extra order of 25,000 horns before Friday's game against Algeria.
Online store Amazon said sales had increased by 1000 per cent since the World Cup started.
David Broughton, from the England-based company thevuvuzelaman.co.uk, said the country was gripped with "vuvuzela fever".
"We sold 1000 online over the weekend. Someone in Dubai has asked for 10,000. If anyone knows of half a million vuvuzelas lying around, they could get very rich," he told British newspapers.
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