The eight-goal striker limped out of the 1-0 win at Charlton at the end of October with the problem and was expected to face close to two months on the sidelines.
But Hill, whose side have toiled in Davies' absence, has confirmed the 26-year-old could return to training on Monday and be involved for next weekend's game at Bolton.
"Craig Davies is in contention to return to training next week, but I don't want to risk any long-term injuries by bringing people back too early," Hill said ahead of this weekend's derby with Huddersfield.
"Touch wood, he is ahead of schedule. It would be a great boost, not just to the team and supporters, but also by the impact it would have on the opposition.
"It has been very difficult to play the way we want to play without Craig Davies in our team. He could be involved against Bolton, but maybe that could be too soon."