The 24-year-old will follow fellow defender Steve Mallory out of the door, as Mallory has departed due to the amount of travelling he is currently undertaking.
Former Scarborough FC centre of excellence player Franks has yet to kick a ball in a competitive match for Boro, his last start being in the 4-3 friendly victory against Bridlington Town in pre-season.
The problem stems from when Franks snapped his medial ligament in his knee a year-and-a-half ago, a problem that hasn’t been resolved.
“It hasn’t been right since my operation,” said Franks.
“For the time being I’m just going to give it a rest and get my knee right.
“I’m not able to train at the moment and I’m not doing myself justice which is frustrating.
“I’ll be having the odd run-out with Hunmanby United in the Saturday League to keep myself fit and I’ll take things from there.
“I thought it would be okay, but it hasn’t been, which is really annoying.
“You don’t want to push yourself too hard though because if things go wrong you could end up not being able to walk later in life.”
Joint-boss Paul Foot added: “We have brought in a few big signings in pre-season, but unfortunately things haven’t worked out as we would have liked with a few of them.
“Leigh’s situation is an example of this.
“We’re gutted that this has happened, but obviously if he does get himself up and running again then the door is open for him to come back.”