The Northern Irishman spent a little over three years at the Anfield helm before being relieved of his duties in October 2015.
He had carried the club close to a Premier League title triumph, but was ushered through the exits after failing to sustain a challenge with the elite.
His departure paved the way for Klopp to move to Merseyside, with the German having now passed the three-year mark with Liverpool.
He has helped to force the Reds back into contention for major honours, but is still waiting on a first piece of silverware.
Rodgers is hoping to see the English top-flight crown returned in 2018-19, telling the Daily Mail: “I want to see them do well, of course.
“For the supporters, it would be brilliant.
“When you think how close we got that time, it became really emotional in that last five games and to go that close and not to win it was tough.
“I look more from a distance now. They will go close. Jurgen Klopp has done a fantastic job and invested well.”
It is not just an association with Liverpool, though, that has Rodgers backing their cause.
He retains strong ties to Klopp away from the field and wants to see him fill his current post for the foreseeable future.
Quizzed on whether it is only human to want a successor to fail after stepping into your shoes, Rodgers said: “It’s only human to ask.
“But Jurgen rents my house. I want him to be there as long as possible!”
Liverpool are yet to suffer a Premier League defeat this season, but will see their title credentials tested again on Sunday when they play host to arch-rivals Everton in the Merseyside derby.
Rodgers and Celtic, meanwhile, will be seeking to land another trophy when they face Aberdeen in the Scottish League Cup final.