The former Brentford boss is on a short-list of potential candidates drawn up by the Light Blues’ board and has reportedly held preliminary discussions with the Govan club.
Rangers are coming to terms with another season in the Championship following their 6-1 aggregate Premiership play-off defeat to Motherwell.
Stuart McCall replaced caretaker Kenny McDowall in March with a mandate to get Rangers promoted to the top-flight but the manner of his side’s capitulation against the Steelmen leaves him with a job to convince the board he is the long-term option.
Warburton, assisted by former Rangers skipper Davie Weir, guided Brentford to promotion from League One last season before taking them into the play-offs this year.
The London side announced in February that Warburton would depart at the end of the season leaving him free to take the Gers post if asked and start rebuilding a squad that will be shorn of at least 10 players.
Warburton said: “From my point of view they are a massive club. I have huge respect for the size of the club and the fan base at Rangers. Who wouldn’t?
“I am well aware of the tradition and history of the club so I would never be anything other than absolutely respectful of a club of that stature.”