Defeat at Stoke on Boxing Day meant the Northern Irishman has exactly the same points haul - 25 - from 19 league matches as that of the now England manager.
Hodgson did not make it past 20 league games as defeat at Blackburn in early January 2011 put an end to a difficult and much-criticised six months in charge.
Rodgers benefits from a position of greater strength as he was the choice of owners Fenway Sports Group in the summer and while his record may not be as good as predecessor Kenny Dalglish, he is working to a different set of objectives than those given to the Scot.
He is a long way from his position becoming under threat and insists progress has been made with plenty more to come.
"I don't think about them to be honest, it is not something I am overly worried about," he said of comparisons with Hodgson's record.
"I have been brought in here to do a job and the owners have been brilliant with me.
"The backing I've had from supporters has been incredible considering and that is the most important group really.
"They recognise what is going on, they understand like I would understand the frustration.
"Any comparisons I don't really focus on and it is difficult to compare the two groups because there is a lot of youthfulness in this group but yet still a lot of growth left in the team.
"There is a lot of progressing to do because we're 10th in the table and this is a club which wants to be at the very top but the only way you can do that is by reconstruction of the work and building the squad.
"That is what is going to take a bit of time. I always say it's like a good meal - I'm not a great cook but a good meal takes a wee bit of time but also to offer a good meal you need good ingredients.
"That is something we will do over time and hopefully put a nice meal on the table for supporters."
A deal for Chelsea forward Daniel Sturridge has virtually been done while the club are still pursuing Blackpool winger Tom Ince.
However, club sources told Press Association Sport "to treat as rubbish" comments by Birmingham chairman Peter Pannu suggesting the club were in talks with Liverpool over goalkeeper Jack Butland.
"I understand there are talks with Liverpool, I understand that Everton might be interested, Southampton gave me an offer in the past, I know not whether they want him," Pannu told the Birmingham Mail.
Speculation has linked Butland with a move to Anfield for weeks but earlier this month Rodgers stressed he was not looking for another goalkeeper in January.
Only a fortnight ago second-choice goalkeeper Brad Jones signed a new contract and while rumours persist about Jose Reina's future it seems inconceivable Rodgers would let him go in January, if at all.
"We certainly won't be able to do everything in January that would help us, but we'll be able to make some additions that will help the group," said the Reds boss.
"We can look forward to that and then review it again in the summer.
"There are very few names we have actually enquired about, but we're hoping we'll be able to do something in January pretty early on.
"We need that wee bit more experience, especially at the top end of the field.
"We're hopeful we can do that and then we'll see what else January can bring for us.
"We won't be spending a great deal of money. It'll be between January and the summer time that we can look at progressing the group and then hopefully go again."