"We've had an informal meeting," he told BBC Scotland.
"It's important to see if there's a chemistry, the parties get on and your football philosophies are aligned."
BBC Sport state that the Light Blues are also considering several other candidates as well, including present manager Stuart McCall, while Rangers legend David Weir, who was assistant to Warburton in West London, may return to Glasgow with the the 52-year-old.
"Any job that myself and Davie Weir would look at would be about going in, having a project and being able to add value," he added.
"But I'm sure a club like Rangers has got a big search process under way.
"I'd like to think we have shown the attributes required to do a good job at a football club.
"Whoever comes in must appreciate the size of the task in terms of the history of the club and where they have to be.
"This is not just about steadying; this is about making significant progress in a designated period of time."
The Englishman is a free agent, having been released from his position at Brentford after dragging the Bees into the Championship and then on to the cusp of the Premier League.
McCall failed with his own attempts to get Rangers into the Premiership, as they crashed to a 6-1 aggregate loss to Motherwell at the weekend in the playoff decider.
Warburton's Brentford side finished in 5th position in England's second tier, meaning they made it to the playoffs, but they were unable to make it past Middlesbrough.
He was due to leave Griffin Park whether he would have taken the Bees into the top flight or not, due to a difference of opinion between himself and owner Matthew Benham. Dutch boss Marinus Dijkhuizen has already taken over from Warburton, leaving him free to discuss his next move.
Sky Sports are reporting that Burnley are also considering the former defender, should Sean Dyche leave the club.