Hughes signed Graeme Smith this month, meaning Stack faces a three-way battle alongside Yves Ma-Kalambay for the goalkeeping jersey.
Hughes said in the Edinburgh Evening News: "Stacky should be back in training in the next day or two, it's not a problem any more.
"We have done everything that has been required and hopefully we won't have any more problems. He's a fit guy anyway and really looks after himself, although he's maybe not been able to do as much as he would have liked because of the nature of the injury.
"If he's back with the rest of the boys then it shouldn't take too long to get him back up to speed. He's been out for a while and we need him to get his sharpness back, so this weekend might be a bit early for him."