Miller is 36 now, but Warburton insists that the striker still has a drive to be successful at Ibrox.
And the Rangers manager insists that Niko Kranjcar will have to show similar levels of passion if he does make the switch to the Light Blues this summer.
“He will have to work hard and he knows that,” Warburton said about Kranjcar. “I went to New York to see him and that hunger and desire shines through. Remember he’s only 31.
“If you saw Kenny Miller train at the age of 36 then you’d realise that the passion burns strong.
“It’s important for a manager to go and see a player and hear the quality of his questions.
“He wanted to know how he could help the club and he wants to win trophies – that’s the important thing.”
Kranjcar arrived in Glasgow yesterday, and he is expected to complete a move to Rangers in the coming days.
The Croatian international would be another high profile addition for Warburton’s side, as they aim to bolster their squad following their return to the Scottish Premiership.
Rangers have already completed five signings this summer, and more new arrivals are expected to follow.
As well as Kranjcar, Rangers are also closing on a deal to sign Matt Gilks and they have also been linked with the likes of Adrian Mariappa and Curtis Nelson.