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.
Rangers manager Mark Warburton believes Brendan Rodgers would be a "great choice" as Celtic's new manager.