35-year-old Cox has discussed a possible move after the former Cardiff City player found himself down the pecking order after losing his place after back-to-back defeats over Christmas to Swansea and Yeovil.
Cox has so far made 19 appearances for the Railwaymen since his signing from Cardiff City in the summer. Julien Baudet partnered him in the centre of defence, but now boss Dario Gradi has switched Billy Jones to operate next to Baudet and Ben Rix has taken over the captain's armband.
Any move would depend on fitness to other players as Crewe take on a hectic schedule which includes the Northern Final of the Johnstones Paint Trophy against Doncaster Rovers.
"It is early days and there has been no interest in him yet. We are considering it and it will depend who comes in for him and whether we lose another defender to injury. But at the moment we would have cover and it would be a chance for Danny O'Donnell and the others to come to the fore."