Caldwell's contract expires in the summer and Celtic are expected to sign the 23 year-old on a pre-contract agreement, before completing the move in June.
Mowbray, who describes Caldwell as "by far the best football-playing centre-back in Scotland," said, "I had a very brief conversation with Gordon many weeks ago and they were just doing the right thing really. There's a procedure when you want to speak to a player.
"I don't know if it's a done deal, I don't know when or if they have spoken to him, so I don't know. All I know is that they're in their rights to speak to him.
"I would imagine Celtic have got more resources than we have and that they could entice him better than we can."
It would be ideal if we could snap Caldwell up in this transfer window, but it looks likely that Caldwell will honour his contract at Easter Road, before making a decision on his future.