Former England manager Hodgson returned to the dugout in January to take over at Watford following the sacking of Claudio Ranieri, but was not able to keep them up.
Hodgson maintains he will not be looking for another managerial job when his time at Vicarage Road comes to an end, with the Hornets set to start life back in the Sky Bet Championship under Rob Edwards following his controversial departure from Forest Green Rovers.
Rodgers is full of admiration for Hodgson’s “phenomenal” career, which has also taken in spells at the likes the Switzerland national team, Inter Milan, Blackburn, Fulham, Liverpool, West Brom and Crystal Palace.
However, the 49-year-old says matching his longevity is not something he currently envisages.
“He is such a reference and role model for us all Roy,” said Rodgers, who himself had a three-year stint in charge at Anfield from the summer of 2012.
“Some 46 years he has been managing, 20 teams, with four national teams and 1,200 games, it is remarkable really.
“Football is about longevity, and it is exactly the same for a manager to have that hunger and desire to keep doing it.
“Roy has proven over many years that he is a top-level coach and I have always enjoyed our conversations, always learned from him.
“To see him still have that enthusiasm and love for the game for that length of time, if you look at Roy’s career, it has been phenomenal.”
Rodgers added: “My target was 1,000 games, get to that and then evaluate from there, but I always knew through that you needed to succeed and have resilience.
“I hope I am not still going at that age, but it is a drug, something that draws you in being around young people and helping them become better and that adrenaline it gives you as well.
“Most managers wouldn’t want to be (still working at that age), but you just never know.”
Rodgers started his managerial career at Watford in November 2008, having left his assistant role with Chelsea.
“It’s always disappointing when one of your former clubs goes down,” said Rodgers, who also had spells at Reading and Swansea ahead of his move to Anfield.
“I have felt for the supporters over these past few years, sometimes you are up and then back down again, but it has obviously been a hard fall in this season.”
Leicester, who reached the semi-finals of the Europa Conference League, sit 10th in the table after returning to form with a 3-0 win over bottom club Norwich on Wednesday night.
“We want to bring our game that we did in the second half against Norwich and if we can do that, then hopefully we can have a good day,” said Rodgers.
“But no matter what team you are playing against, no matter what the situation is, there are always moments in the game that are going to be tough for you.”