The 26-year-old Spain international has been the subject of persistent speculation linking him with a big-money move away from Anfield this summer.
The trio have all been mentioned as potential destinations but new boss Hodgson, having met Torres this week, has emphasised his determination to keep him.
Hodgson took charge at Liverpool a fortnight ago but was unable to meet Torres at first due to the player's involvement in the World Cup in South Africa.
Speaking at his team's pre-season training camp, Hodgson said: "I have met with Fernando.
"I found him to be a very pleasant man and we had a nice conversation.
"As far as we are concerned he is a Liverpool player and we want him to remain a Liverpool player.
"He is not for sale and we don't welcome any offers for him. We want to keep him.
"My conversation with him was only short because I had to leave to come to the training camp in Switzerland.
"We spoke about football, the World Cup, his injury, and I told him how much I am looking forward to working with him.
"Christian Purslow [managing director] was also at the meeting and chatted to Fernando for a lot longer after I left but my chat with him was only about football matters."
Liverpool officials flew to Spain to meet Torres this week to assess the injury he sustained in the World Cup final last weekend.
Torres suffered a slight tear in an adductor muscle in the closing stages of Spain's glorious defeat of Holland in Johannesburg and will be out of action for another three weeks.
That rules him out of much of Hodgson's pre-season plans, and a two-legged Europa League qualifier, but he had been granted a three-week break due to the World Cup anyway.
Liverpool are still hopeful Torres will be fit for their Premier League opener against Arsenal on August 15.
Hodgson was equally forthright on the subject of captain Steven Gerrard's future but the picture concerning Argentina skipper Javier Mascherano is unclear.
The pair, who have not begun pre-season training yet either, have also been linked with moves elsewhere.
Gerrard is rumoured to be a target of Real Madrid while Mascherano's agent has claimed Inter Milan are interested in his client.
Hodgson said: "I have met with Steven and thought the talks were positive.
"We are in a situation where we hear our players are being courted by other teams but it is all just rumours.
"What we haven't had is a club wanting to buy Steven Gerrard. Steven Gerrard is not for sale - I made that clear to him.
"I told him I supported the club's policy that we don't want to sell our best players and have to start building again."
He added: "I have tried to contact Javier. I have left him voice messages and sent him texts but had no reply.
"To be fair to him, that's not unusual because he's had a tough World Cup and I believe he's gone back to Argentina.
"It's not always easy to get in touch with people. I have tried to reach him to make clear I am happy to talk with him at his convenience."