The Spain international was linked with the Reds' arch-rivals earlier this week and Arsenal have been mentioned as potential suitors in the past.
Speculation over the future of Reina - and other star players - has arisen because of the recent instability at Anfield and the poor start made by the club to the Premier League season.
But the 28-year-old only signed a six-year contract in April and Hodgson has no intention of letting one of his most prized assets leave.
Hodgson told the Liverpool Echo: "It was just one of those stories that seems to occur - it's just disappointing and annoying.
"Pepe is fantastic here, he is a lifeblood of this team.
"Everything he does around the club is excellent - he is always lively in the dressing room, he is always first class in training and he always wants to do more to improve.
"He demands better from those around him, he is always pushing people on. He is a player who we hold in the highest esteem.
"We have heard nothing from Manchester United and, more to the point, we don't want to hear anything from Manchester United.
"If (Sir Alex) Ferguson is looking around at the end of the season and he has got lots of money to replace (Edwin) van der Sar, he might very well want Pepe Reina because he is the best around.
"But we do not want to sell him. I would like to think that we are going to become a successful club once again and Pepe is crucial to that."
Forward Dirk Kuyt is making encouraging progress in his recovery from an ankle problem and could be fit to face Chelsea a week on Sunday.
Kuyt was expected to be sidelined for a month after sustaining the injury on international duty a fortnight ago.
Hodgson said: "He shouldn't be as far advanced as he is with his ankle but he's looking good. I don't think he'll be fit for the weekend but maybe the weekend after."
Full-back Glen Johnson has an outside chance of returning for Sunday's trip to Bolton after missing three of the last four games with a thigh injury.
Ryan Babel has been cleared of serious injury after taking a blow to the ribs in a reserve match this week.