Reports have suggested that the Spain international, who signed a new six-year contract with Liverpool towards the end of last season, had expressed a desire to quit Anfield.
However, the 28-year-old has insisted this is 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.