It is the first time that a Fifa official has admitted in such stark terms that not everything is going to plan for South Africa, the first ever host of the tournament on the African continent.
However, Andy Richardson, Al Jazeera's sports presenter, said: "While I was there [in South Africa] in December, Soccer City was very, very close to being ready and I am sure it will be ready ... so I don't think we should get too worried about the facilities."
Last week Fifa slashed the prices of some unsold VIP tickets in the hope of selling them to South Africans rather than overseas fans.
"This was a promise that Sepp Blatter [the Fifa president] made to the South African government," Valcke said.
Category-four seats, the specially-priced tickets for South African residents, sell at 140 rand ($18.21).
Valcke said 11 per cent of stadium capacity was currently made up of category-four tickets and Fifa hoped to increase this to 20 per cent for most games at the June 11-July 11 finals.
"We will do our best to get up to 20 per cent for most of the matches but we will not discount any ticket prices and we'll not give any tickets away. There will never be a free ticket for the World Cup."
He said he expected ticket sales to cover the $423m budget for organising the World Cup in South Africa.
"We are trying at a difficult time for the world," Valcke said.