Hodgson's days at Anfield have been widely reported in the British media to be numbered after a miserable season featuring nine league defeats which has left them just four points above the relegation zone in 12th place.
He takes his team to traditional rivals Manchester United on Sunday for an FA Cup third round match where defeat could finally cost him his job.
That issue was the elephant in the room when Hodgson gave an in-house interview rather than a pre-match news conference, answering questions on injuries and players' spirits rather than on whether a win at Old Trafford would save his job.
"Due to the media speculation surrounding the club, it was decided that a formal press conference was not appropriate in the circumstances," a Liverpool spokesman said.
In comments published on the club website, Hodgson said Sunday's high-profile game offered his team the chance to put Wednesday's 3-1 defeat by Blackburn Rovers behind them.
"This game against our fiercest rivals gives us the chance to show we are better than we were on Wednesday," he said.
"We've got quite an experienced bunch of players here and they know as well as I do how important this game is - in particular for the supporters of the club who'd take enormous delight if we could knock Manchester United out of the Cup on their home ground. It would be a remarkable coup."
Poor defensive performance
He said it would require "intelligent football" to beat the Premier League leaders and that he expected an improved performance from his players after a "poor, poor defensive performance" in their midweek game.
"We're not going to do it through heart alone," he said. "It needs to be a combination of endeavour and desire but also people using their heads to play well tactically, negate Manchester United's strengths and take advantage of some of their weaknesses."
The Anfield boss is hoping defenders Paul Konchesky and Martin Skrtel will be fit for the game after sustaining a dead leg and stomach strain respectively and added that he expected a great match.
"Manchester United versus Liverpool at Old Trafford - it doesn't matter what occasion it is, it's always going to be a cracker," he said. "It's always going to get people talking and on the edge of their seats."
Whether they are talking about the action on the field or the ramifications for Hodgson off it after the game remains to be seen but win or lose it will not be for want of trying.
"It's very important the fans realise that we understand they have high hopes, expectations and ambitions for the club and the team. We have high hopes, expectations and ambitions as well," said Hodgson.
"Every time we go on to the field we desperately want to see those dreams materialise and to produce the performances which bring you results. It's very painful when it's not happening and the fans make their views felt."
