Parry, 24, has made two appearances for Barrow during a loan spell from the League Two club.
The former Southport and Telford player, who can also play in midfield, had a spell at league rivals Altrincham earlier in the season.
Bluebirds boss Paul Cox is hopeful of adding a further signing to his squad.
Meanwhile, Luton boss Nathan Jones says he "expects a quiet transfer deadline day", having already signed defender Alan Sheehan and forward Joe Pigott, while Luke Guttridge and Luke Wilkinson have left to join Dagenham and Stevenage respectively.
National League Barrow have signed midfielder Andy Parry on a deal until the end of the season following his release by Luton Town.