South Africa's Football Association (SAFA) held talks with Parreira on Friday amid reports the Brazilian was about to quit and return home.
"I cannot comment on this report until further notice," Parreira told AFP in Johannesburg.
Raymond Hack, SAFA's chief executive, said he was surprised by Parreira's wife's comments.
"As far as we are concerned, Parreira is our coach and has signed a contract to coach Bafana Bafana until after the 2010 World Cup final," Hack told SAPA news agency.
|"I cannot comment on this report until further notice." |
Carlos Alberto Parreira
"However, tomorrow is another day and who knows what will happen?"
However a close friend of the 65-year-old Brazilian, speaking on condition of anonymity, said Parreira is quitting because he dearly misses his family and spends a fortune telephoning them.
Parreira, who guided his homeland to the World Cup title in 1994, rushed back to Brazil in February when his wife underwent undisclosed surgery, and she told Folha her husband intends leaving South Africa next month.
"He has already made his decision and is set to return to Brazil at the beginning of next month," Leila Parreira said of her husband.
After a slow start with Bafana Bafana (The Boys), Parreira was hailed last month when South Africa thrashed Paraguay 3-0 near Pretoria in a friendly.
The much-needed win came after they were eliminated in the group stage of the Africa Cup of Nations in Ghana earlier this year.
South Africa are only 71st in Fifa's world rankings.
The 65-year-old has coached a number of other national teams, including helping Kuwait and Saudi Arabia qualify for World Cup finals.
The uncertainty over Parreira's future is the latest cloud over South Africa's preparations to host the World Cup.
Rising levels of violent crime and worries about a blow-out in construction costs for stadiums and other infrastructure have raised fears the African nation will be unable to make a success of hosting the 2010 tournament.