Spain's chances at the World Cup took a knock as Liverpool striker is ruled out of the opening games by Liverpool medical staff.
The 26-year-old is recovering from surgery to repair knee cartilage torn in the 4-1 win over Benfica on 8 April.
"Whether he will be fit for the first game or not is uncertain," said Peter Brukner who is overseeing his recovery.
"But, if he continues to progress the way he is, he should be fit to play at some stage during the World Cup."
Spain, current European champions and one of the pre-tournament favourites, play their first match in Group H is against Switzerland on 16 June.
Games against Honduras on the 21 June and Chile on 25 June then follow.
If they progress to the knock-out stages, Spain will play a second-round match against one of Brazil, Portugal, Ivory Coast or North Korea on the 28 or 29 June.
Boss Vicente del Bosque also has injury concerns over midfielder Xavi who is playing through a calf tear that may see him ruled out of the World Cup.
The 30-year-old is playing on in an attempt to help Barcelona hold off Real Madrid's challenge and win a second successive Spanish league title.
But del Bosque said although he was worried about Torres, expectations for his recovery were good.
"I am sure that when the moment comes all the players will say they are fine but we are the ones who have to evaluate and decide the risk that should be taken," he said at a Spanish soccer federation event in Madrid.
"We cannot go to South Africa with four or five doubtful players," he added. "We have good hearts but we have to listen to our heads."
Bruker, who was appointed as Liverpool's head of sports medicine and sports science in March, believes there is a balance to be struck between the demands of club and country for Torres.
"He is certainly tremendously committed to his rehab, as are the staff here, and if anyone can recover from an injury, he can," he said.
"Hopefully we can get a compromise where he plays in the World Cup and he is fit and well for Liverpool next season."
Torres spent a month on the sidelines after a knee operation in January and was hampered by a troublesome groin injury before Christmas.
Despite the disruption, the former Atletico Madrid forward has scored 22 goals in his third season for the Reds, including 18 in 22 Premier League appearances.
Torres has an impressive record at international tournaments, scoring three goals in four games in the 2006 World Cup and the winner against Germany in the Euro 2008 final.
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