The former Derby County midfielder may be the next arrival at Ibrow after flying into Glasgow for talks with Mark Warburton.
Eustace admitted that though he hadn't committed to joining the Scottish giants, he was going to discuss a possible move with new Rangers boss Mark Warburton, with his contract at Pride Park expiring this summer.
What the 35-year-old did admit to was how excited he was after hearing about the former Brentford manager's plans for taking the Gers back to the top of Scottish football.
"I’m just here to meet the manager and see what it’s all about," he told Sky Sports.
"He said it’s an unbelievable place and it will be a very exciting time over the next few years.
"It’s exciting, it’s one of the biggest clubs in Europe."
The midfielder did discuss his match fitness ahead of a possible move, which may end up being Rangers' third move after the signings of Danny Wilson and Rob Kiernan.
"I’m still a few weeks off," Eustace said when asked about what kind of fitness level he had ahead of pre-season. "I’ve only just started light running."
The player missed most of last season with Derby with a serious knee injury, with many pointing to his absence as the reason the Rams faded so badly in the second half of the season.
Whether Eustace signs up at Rangers in the coming days, or bides his time before a possible arrival, the club would clearly benefit from getting someone with his experience and influence in to help the Gers make that final step back to the Scottish Premiership.