The Hibs midfielder has been at the heart of one of the biggest transfer sagas this summer.
"In truth, we only want players who want to be here and want to play for Rangers,” said Warburton, in quotes published by STV.
"So I wish any player well but right now our focus is on making sure we secure those players, with that mindset, who want to be here.”
When asked if he had ever had conversations with the Hibs midfielder during Rangers’ summer pursuit, he said:
"He’s not my player. As simple as that, it would be disrespectful to say anything other than that he’s not my player and it’s not for me to talk about."
The Rangers boss was in defiant mood and made it clear that the club will not be wallowing in the failure to capture one of their key targets.
"If a player doesn’t want to be here, no problem,” said Warburton.
"We move on, and we have moved on very quickly as you’ll see with what we’re doing right now and what we’ll do next week. We’re in good shape."
Despite his insistence to the contrary, the former Brentford boss is sure to have felt a pang of anger when news broke of Celtic’s bid.
Allan is just the type of creative, attacking midfielder Rangers need to ensure they get the goals this season, and his experience of the Scottish championship makes him an even more attractive proposition.
Confirmation of his move to Celtic now appears imminent – with BBC Sport reporting that the deal was complete, subject to the player's medical today – and Rangers must now look elsewhere in their bid to build a squad capable of gaining promotion to the top flight, at the second time of asking.