The Socceroo star, who has been the fulcrum of Huddersfield’s fairytale promotion to the Premier League last May, is currently sidelined by an infection in the knee, which he cut during the 4-1 home win against Bournemouth earlier this month.
Mooy had returned to his all-action best against Bournemouth after a dip in form in recent weeks.
But he missed last weekend’s FA Cup home defeat against Manchester United and will also sit out this weekend's pivotal trip to bottom-placed West Bromwich Albion.
The 27-year-old is also likely to miss the trip to Tottenham Hotspur at Wembley, but the date with fellow relegation-threatened side Swansea should see his return, according to Wagner.
"Aaron started his gym-based work and cardio vascular-based work two days ago," Wagner said.
"I think, or rather we hope, he will be in individual training on the field in the middle of next week.
"There is a question mark over whether he will be ready to face Tottenham, but we are pretty sure that he will be available after that for the Swansea game."
Mooy's return will be a timely boost for the Terriers next month as they currently sit in 17th, just one point above the dropzone.
Huddersfield will move 10 points clear of last-placed West Bromwich Albion with victory this weekend, and Wagner is in confident mood.
Albion’s plight has been worsened by their recent off-field troubles which saw four senior players accused of stealing a taxi in Barcelona.
Manager Alan Pardew is also coming under growing scrutiny after conjuring just one win since replacing Tony Pulis three months ago.
"For sure Alan didn't like what happened last week with the incidents, but it's West Brom's problem and doesn't bother us," Wagner said.
"Hopefully we can shake hands after the game with three points in our backpack. All the teams that are engulfed in this battle to stay up, the pressure is on them.
"There are clubs with bigger names and much bigger budgets where the pressure is even bigger – but we want to stay up. This is what we have fought for since pre-season."
