The npower Championship side were in talks with Town over a move for the 25-year-old, but the clubs were unable to come to an agreement.
Crawley chief executive Richard Low told the club website: "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."
McFadzean, who was linked with moves to the Championship during the previous two transfer windows, is currently sidelined due to the effects of a virus.
Low added: "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."