The Scottish club reportedly remain interested in a deal for the 27-year-old, who officially left Town this summer.
After four appearances last season, the 27-year-old was loaned to Championship rivals Birmingham in November, and the deal was extended in January.
At that time, an agreement for a St Andrew’s contract to cover 2016/17 was put in place.
But Rangers are said to be interested as they prepare for their Scottish top-flight return.
Vaughan has no guarantee of first-team football at Birmingham and will talk to gaffer Gary Rowett when the club return to training next week.
Ibrox boss Mark Warburton has already signed former Town duo Matt Crooks and Josh Windass.
Croatian Nico Kranjcar is poised to sign a two-year deal and will join fellow new boys Joey Barton (Burnley) and Jordan Rossiter (Liverpool) in midfield.
Centre-back Clint Hill has joined the Gers from QPR and Warburton is set for talks with Burnley keeper Matt Gilks.
It’s said Warburton wants Vaughan to provide competition for frontmen Martyn Waghorn and Kenny Miller.
The injury-plagued former England Under 321 international scored 33 goals, including two hat tricks, in 95 Town games.
The Everton product joined Town on loan from Norwich City in August 2012 and the move was made permanent in a £600,000 deal the close-season after.