The League One club did not go into specific details on why City have cooled their interest in the 25-year-old central defender.
Crawley chief executive Richard Low said: "There has been a lot of speculation about Kyle in the last few days and, as everyone knows, we were having ongoing discussions with Bristol City.
"They have now pulled out of any deal to sign Kyle so he remains a Crawley Town player which is obviously great news for everyone at the club.
"Of course the transfer window is open for another seven days and who knows what might happen but Kyle is happy here and is working hard in the gym to get his fitness back and we hope he will be back and available for selection soon."
Bristol City manager Sean O'Driscoll later revealed that the Championship club remain keen on McFadzean, but that they will not be pursuing him further until the end of the season.
O'Driscoll said on the club's Twitter feed: "To end speculation, there's still an interest in Kyle McFadzean but, given our situation, it's more likely for the summer."