And the Anfield giants now fear they face a battle to hang on to their £70million-rated Spanish striker.
Torres, 26, refused to confirm he will stay, saying: "I have a contract... it is the reality now."
He plans to meet Hodgson once Spain's World Cup campaign is over.
Torres, who faces Germany in Wednesday's semi-final, has three years left on his deal but is a target for Chelsea and Barcelona.
Speaking for the first time since Hodgson's appointment, Torres said: "I haven't had a chat with him yet but I will talk with him soon and we will see his ideas about the future.
"My future is here in South Africa. The World Cup is too important to think after that.
"I will talk with him soon. I have a very important week still here and after that I will have time to talk with him about my future."
Torres' Kop career has been in doubt ever since Liverpool missed out on a Champions League place.
SunSport understands he is unhappy at the way the club is run and puzzled it took until last Thursday to appoint Rafa Benitez's successor.
The uncertainty surrounding the Kop's American owners and the lack of cash to strengthen the squad this summer are the main reasons for Torres thinking of quitting.
Manchester City are also keen to capture him but have little chance after they, too, failed to qualify for the Champions League.
Liverpool will compete in the Europa League next season, a competition which saw Hodgson take Fulham to the final in May.
Torres insists the new boss can repeat his success on Merseyside.
He said: "I was happy Roy Hodgson got the job. He did really well at Fulham and I am sure he can do better for Liverpool.
"He is a very good manager. Hopefully, he will be the right man to give Liverpool the opportunity to be strong again."