The Leeds boss wants to right one of the club's wrongs from this season.
Without issuing an ultimatum either way, the Leeds head coach stated that the potential return of his no.2 is something it would be 'important' for him to know could happen.
Thompson was Redfearn's assistant manager for several months this season, with the Yorkshire side at times displaying promotion form while the duo were at the helm.
The no.2, however, was suspended some weeks ago - with absolutely no explanation given as to why to this day.
A suspension is not permanent, though, and Redfearn has called on Leeds to allow him to bring his assistant coach back. That factor will be crucial to his Elland Road future.
The 49-year-old told reporters: "That’s got to be resolved. Steve’s been suspended but I don’t think there’s been an inquiry since. It would be nice to know what’s at the bottom of it. It would be good if I could get Steve back.
“That for me would be a big plus and I think it’s important for me to know that that would happen. Steve came in and made a big difference. We worked well together. For me going forward, as a pair we compliment each other well. If we could do something about that it would be a big plus."
Leeds face Rotherham United on the last day of the season, a game that will be Redfearn's last in charge of the Yorkshire club should he and Italian owner Massimo Cellino fail to agree a new contract for the manager.