The pair worked together at Watford and Northern Irishman Rodgers, 43, is the frontrunner for the Celtic job after two rounds of talks this week.
Celtic's largest shareholder Dermot Desmond said on Wednesday "in excess of six" candidates had been interviewed for the manager's position.
"There's no doubt about his qualities," said Warburton, 53, of Rodgers.
The Englishman was a coach with the Hornets during Rodgers' time as manager, with the latter subsequently having a spell in charge of Reading and then leading Swansea to promotion to the Premier League.
A move to Liverpool followed and Rodgers left Anfield in October after over three years in charge.
Warburton is preparing his Rangers side to face Hibernian in Saturday's Scottish Cup final.
The Englishman has already won the Championship and Challenge Cup in his first season in Glasgow.
And, after overcoming eventual Premiership champions Celtic in this season's Scottish Cup semi-final, Warburton's Rangers will face their Old Firm rivals in next season's top flight.

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The news of Annan Athletic's 4-1 fourth-round win over Hamilton Academical was far-reaching.
Omar, the son of refugees from Iraqi Kurdistan, was featured in the local press there.
"There's a big following there now, my uncle tells me," said the Glasgow University student.
"A lot of them, when they are looking out for scores, will look out for Annan Athletic now."
Annan's dream ended in the fifth round though, when they lost 4-1 to Morton.
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The 24-year-old, capped 32 times by England, has been out of action since November with a knee injury.
However, it is understood his recovery has progressed quicker than expected.
Vunipola could now be in contention to face Scotland on 11 March, or Ireland a week later.
He was one of England's outstanding performers throughout their unbeaten year of 2016, and his ball-carrying and dynamism has been missed by Eddie Jones' side.
There were initial fears Vunipola would miss the whole of England's Six Nations title defence, but it is understood he has looked sharp on his return to full training this week, and is targeting a quick return to international rugby.
Vunipola's older brother, Mako, recently made his own comeback from a knee problem, and came off the bench in the win over Italy.

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The 17-year-old from Gloucestershire won the champion apprentice trophy in his maiden season this year.
Marquand has racked up 68 wins across the last 12 months, prompting his trainer Hannon to make the comparison with Moore.
"I think he could be a champion jockey one day," Hannon told BBC Points West.
"I would be amazed if he does not go right to the top, he is the name on everybody's lips at the moment."
Marquand's rapid rise has seen him nominated for the BBC Young Sports Personality of the Year 2015 award.
The jockey has been named on the final shortlist for the award, alongside gymnast Ellie Downie and para-swimmer Tully Kearney.
"What he has achieved is a little bit special," added Hannon. "He is a lovely guy and thoroughly deserves his success. He is very popular and he has endeared himself with everybody."
Hannon, who has 300 horses based at his stables near Marlborough, is the son of former flat jockey champion Richard Hannon Sr.
Moore has enjoyed great success under the guidance of Hannon and won the champion apprentice title in 2003.
Since then, Moore has established himself as one of the most respected flat jockeys in horse racing and was champion jockey in 2006, 2008 and 2009.
"Ryan Moore performs on the big stage and he is the best jockey in the world at the moment. He is so professional and the ultimate jockey and that's who you want to be," said Marquand, who will find out if he has won the BBC award on Sunday.
"It is a yard that is constantly in the limelight and it is big to be attached to somewhere like this."
Rangers manager Mark Warburton believes Brendan Rodgers would be a "great choice" as Celtic's new manager.
[NEXT_CONCEPT]
Goal hero Rabin Omar made headlines when his club from the fourth tier of Scottish football dumped a Premiership side out of the Scottish Cup.
[NEXT_CONCEPT]
England number eight Billy Vunipola is set for a shock early return to action for his club Saracens against Newcastle on Sunday, boosting his hopes of a 2017 Six Nations call-up.
[NEXT_CONCEPT]
Teenager Tom Marquand has been tipped to follow in the footsteps of three-times champion jockey Ryan Moore by his trainer Richard Hannon.