The 20-year-old Welshman has signed for local non-league club North Ferriby United until the end of the season.
Price has failed to make the City starting eleven all season, and his only appearance off the bench lasted a matter of seconds, coming on in injury time of the opening day win at Exeter.
The Welsh U-21 international now joins the Unibond First Division side in hope of getting his form and fitness back.