Cox, who was made club captain after his summer move to Gresty Road, has asked to be allowed to leave the club in search of first-team football.
The 35-year-old has struggled to form a good central defensive partnership with Julien Baudet, and will be allowed to move - temporarily - from the club.
"I had great hopes for Neil and Julien, but they have not done particularly well together," admitted Railwaymen boss Dario Gradi.
"We conceded a lot of goals, and it appears better with Billy Jones in the centre. I could use Neil in midfield, but the easier solution is to allow him to go out on loan.
"He is not going to get in the side at the moment, but is fit and, at his age, wants to play."