The sport's governing body announced on Wednesday that an unidentified European race had been pencilled in for July 21, subject to the agreement of national bodies, to bring the calendar up to 20 races.
Turkish race organisers have said staging the grand prix would depend on whether the government made funds available. Local media reported the Istanbul track operator as saying the government would provide $13.5 million in funding.
But Sports Minister Suat Kilic told reporters on Thursday the race was purely a matter for the private sector.
"If it wants to, the private sector can bring Formula One," Kilic was quoted as saying by the Dogan news agency.
"But there is no question of us paying the cost of the rights which have been proposed to a private company to bring Formula One."
The Turkish Automobile Sports Federation said that the grand prix - last held in 2011 before being dropped after a disagreement over hosting fees - had been discussed at a meeting of the International Automobile Federation in Istanbul.
"We in TOSFED are making every effort so that Formula One races, which have been held seven times in our country until now, can be held at our Istanbul Park track...(in 2013) and in future years," chairman Demire Berberoglu said in a statement.
Berberoglu said an agreement had been reached between circuit operator Vural Ak and Formula One supremo Bernie Ecclestone, but the government also had to play a part.
"Everybody knows that what is needed for its presence in the Formula One race calendar for 2013 and following years is a guarantee and approval of the required budget at the government level," said Berberoglu.
"This will develop according to the prime minister's decision."
Kilic said the government had previously assisted in bringing Formula One to Turkey, making a "sacrifice" in order to boost the sport.
"Our government paid $13.5 million a year to the organisers for five years for the rights. In exchange for that, all the income went to the organisers, so the state did not get any benefit from it," he said.
The Istanbul Circuit, on the Asian side of the city, was highly regarded by teams and drivers for its challenging layout but the race failed to attract much local interest.
Its reinstatement next season would plug a gap left by the postponement to 2014 of a Grand Prix of America that was due to be held in New Jersey.
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