Wallace pulled out of the squad for the World Cup qualifier against Croatia with a knee injury but has an outside chance of facing Brechin in Saturday's
Scottish League One clash at Glebe Park.
Gers manager Ally McCoist told the club's official website: "Lee had the scan and we got the results late last night. We had a look at them and they're not too bad thankfully.
"We're very, very hopeful he can start training again in a couple of days, although I'd have to say he'll be a doubt for the weekend.
"You never know though and he's a fit lad who'll give himself every chance to play because he'll certainly want to play, that's for sure. We'll see how things go."
But Wallace's fellow defenders, Perry and Hegarty, are both struggling to recover from ankle injuries. Perry has not played yet this season, while Hegarty has been out for two months.
"Sadly both Ross and Chris have had setbacks and they've each been to see the specialist once again," McCoist added.
"We're just monitoring them with our physios and the doctor and it's as much a mental thing for the two of them now as anything.
"The blows they've had will be of massive disappointment to them but they'll have to handle that and they've a terrific unit in here that will help them along.
"We've been there ourselves with injuries and we know how depressing it can be so we need to give them the support they need, encourage them and hopefully they'll heal soon."