British media reports claim that the club's new American owners have already decided to replace Hodgson and are merely biding their time to ensure they get the right man.
GEAR:Save 22% on Liverpool home shirts with Kitbag. Free delivery on orders over £50
Having been brought some breathing space by Joe Cole's last-minute winner in Saturday's 2-1 home victory over Bolton Wanderers, Hodgson, who replaced Rafael Benitez before the start of the current season, told the club's website that he needed time.
"Being honest about it, I am hoping that one day I will get a chance to stamp a little more of my authority and philosophy on the team by choosing some more of the players," Hodgson said.
"It is not often mentioned, but I have not been that active in the transfer market since I have been here.
"The players who are playing are the ones you have watched playing for the past few years. They have done exceptionally well for me in accepting a new manager, with a new style and a new training method, and giving the performances they have given, albeit that unfortunately we have been guilty of inconsistency."
Liverpool are currently ninth in the standings, already 16 points behind leaders Manchester United with their hopes of a first league title since 1990 long gone.
Two seasons ago they were top of the league going into the New Year and, having seen Benitez moved on, the fans are hugely frustrated that their club has made no progress under the new man.
Hodgson was appointed by the former owners and the new bosses have changed the management structure by bringing in Damien Comolli as director of football strategy.
RESTING STARS
Comolli is likely to have a major say in any transfer deals, something Hodgson will be well used to having worked under similar systems during his many and varied management stints around Europe.
Hodgson, however, is not expecting a major influx of players in the January window and says the squad he has needs to start making a difference and needs to be led by their three world-class players - Steven Gerrard, Fernando Torres and Pepe Reina.
"If we are going to win games it is the Torreses, the Gerrards, the Reinas, that are going to be the ones to get us up the table and lift us above the rest," he said, adding that the two outfield men would have to be nursed through a gruelling fixture list.
"Fernando had a very serious knee injury, which seems to be in the past, but when you have had an injury there is always the little risk of recurrence. And Steven, of course, is susceptible to muscle injury if he plays too many games one after the other.
"I have just got to hope that the ones who just seem to keep going - the Duracell bunnies like Dirk Kuyt and Lucas Leiva - can keep us going and give me a chance of giving a rest to the others.
"But it is the same for all the teams in the league.
