The 35-year-old former Watford midfielder is a free agent at the moment, having left Championship outfit Derby County at the end of the 2014-15 season.
Eustace has been training with Scottish Championship club Rangers over the past three weeks in order to regain full fitness with a view to signing a contract with the Gers.
Warburton has suggested that the Gers will hand the former Stoke City man a deal, claiming that he would be a great leader.
“John has trained well,” the 52-year-old told The Scottish Sun. “He’d be a great leader, along with the likes of Kenny Miller, Cammy Bell and Lee Wallace.”
Rangers have been busy in the transfer market so far this summer, signing no fewer than seven new players.
Goalkeeper Wes Foderingham (free), central defenders Danny Wilson (free) and Rob Kiernan (Wigan Athletic), winger Andy Halliday (free), forward Martyn Waghorn (Wigan Athletic), right-back James Tavernier (Wigan Athletic) and Jason Holt (Hearts) have all been already snapped up by the Glasgow outfit.