The central midfielder had been on the verge of signing for the Owls from Bolton Wanderers.
Davies has been at Bolton since 2009 but the Lancashire club are struggling financially, and results on the pitch are no better.
Sheffield Wednesday have numerous options in midfield, but Davies, 27, would have provided key experience to help the club's promotion push.
There is of course still a chance the deal gets resurrected, but for now it appears the switch has hit a stumbling block, and the Owls must decide whether to pursue new targets or try to salvage the move.
Bolton are currently on course to be relegated while Wednesday are battling to make the play-offs.