Reports had suggested the Spain international, who signed a new six-year contract towards the end of last season, had expressed his desire to quit Anfield.
However, the 28-year-old has said this was untrue.
"I have not told the manager that I wish to leave in January or at any time," he told liverpoolfc.tv.
"It is important our fans know this. I have a long-term contract at the club and am fully committed to the club."
Reina added: "I have seen a newspaper has made this suggestion. It is completely untrue."
Rumours about the goalkeeper's future have been circulating since the summer - when Arsenal were linked with a bid - but intensified this week when he was reported as claiming he would look at his position at the end of the season.
When asked about it on Tuesday Hodgson shrugged it off, saying the player was entitled to assess his position.
"That's fair enough, what's wrong with that," he said. "He is an excellent goalkeeper and I hope he plays for Liverpool for years to come."
Liverpool have had to cope with a huge amount of speculation this season in particular, partly caused by the uncertainty of the ownership.
However, once New England Sports Ventures completed their £300million takeover last month a degree of stability has been brought to the club both on and off the field.
And Reina insists the players will not be distracted by rumours, having met with NESV principal owner John Henry only last week to talk about the way forward.
"Our new owner met me and some of the other players last week and I was very happy with what he told me," he added.
"The entire squad and staff are working very hard to get us back competing at the top of the table.
"We will not be distracted by inaccurate media speculation."