However, despite terms being agreed, Holt rejected the move after being requested to play in a trial match before the deal went ahead.
He now returns to training with the rest of the squad, and made his first pre-season appearance against Scarborough on Wednesday.
But Greg Strong - also on the transfer list along with Holt and defender Shaun Smith - has agreed to join Bury on a two-month loan.
City boss Peter Taylor said: "Greg has got very close to our first-team and, to be fair to him, I can't fault his attitude and his commitment.
"However, he's told me he wants first-team football and I just can't guarantee him that. It's a shame, but these things happen.
"I will hold my hands up and admit that he hasn't really had a chance with me but I've said I couldn't really pick him ahead of people like John Anderson, Justin Whittle and Marc Joseph - especially after last season.
"We're well off for central defenders so hopefully the move will benefit everyone. We haven't shut the door on Greg and at least the move will give him the opportunity to start playing again."