The former Liverpool boss has been interviewed twice by the Hoops’ hierarchy and appears to be the frontrunner in the race to replace Ronny Deila.
Warburton knows the 43-year-old from their time together at Watford and has no doubt he can handle the intensity of working in Glasgow’s east end.
The Ibrox manager - speaking at the pre-match media conference for Saturday’s William Hill Scottish Cup final with Hibernian - said: “I know Brendan, I worked with him at Watford. I was academy manager and he was manager.
“He’s very experienced, well organised, a good motivator, a good man-manager. He’s a manager of the highest quality.
“He’s worked in the Premier League and came within a slip of winning it, so there’s no doubting Brendan’s qualities.
“I like him very much as an individual, so if he is the man, he would be a great choice.”
Celtic majority shareholder Dermot Desmond - who hopes to wrap his search within the next week - has already admitted Rodgers would be a “great” choice for the post.
Former Celtic defender Malky Mackay is also understood to have been interviewed in recent days, while the likes of David Moyes, Neil Lennon and Roy Keane are still in the running too.
But Warburton insists his side will be ready to battle with their old foes upon their return to the top-flight next year, no matter who is in the Hoops’ dugout.
“You have to enjoy the challenge,” he said. “Whoever Celtic choose, it’s about Rangers and how we prepare for the challenge they pose.
“There’s no doubt Celtic will pose a real challenge next year. We have to rise to that.”
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