Nor will Sam Hutchinson be, as the Owls look to tread carefully with his injury.
Meanwhile Lewis Gibson's time at Sheffield Wednesday could be coming to an end, with the ominous news that the Owls will have talks with Everton about their loanee, who was injured in the first half of his League One debut for the club.
Luongo has played twice this season, in August, before injuring his hamstring. Of fellow midfielder Byers's five appearances, only one has come since, at Plymouth Argyle. He had a groin problem. Things are looking up for both, though.
"We're pleased that Mass and George are back into real full training now, full contact," said manager Moore.
"We're going to give them a bit of volume. They'll both play for the Under-23s on Monday night, which is excellent.
"It's great to have them back on the training pitch.
"Mass - as is George - is a really important player because they're different to the midfield players we've got in now.
"To have those two back, available and ready, hopefully they come through unscathed in the next couple of weeks because that will be a real positive for us."
Windass is also stepping up his rehabilitation, though from further back having not played since hamstring surgery in the summer.
"Josh is back out amongst the group doing some lighter work and it's great to have him back," said Moore. "I always think when a player feels the grass again there's light for him. It's great for to have him back but we'll monitor him with the sports scientists and the medical team.
"He's looking good, he's looking great and to get back with the boys is a massive psychological boost for him."
Hutchinson, though, remains out.
"He's had a minor setback with his recovery - too much too soon in training, nothing out of the ordinary, just his eagerness to get back to it," he said. "We've had to taper him off a little bit.
"It was through the hard pitches. We just think he's had a little bit of a muscle strain. He played the (Bolton) game and he just pulled up with it so since that we've tried to get him back into and it's not settled as we'd have liked. It's nothing too serious but we've just got to ease off with him because of the volume of games coming up.
"Every game we're just assessing him and if he's symptom-free, we're good to go. If he's feeling a little bit of tightness I don't take the risk. As much as we'd like him back we want him back for a longer period."
No decision has been made on Gibson, but there was a long pause when Moore was asked if his Hillsborough future was in doubt before replying: "Right now it would be wrong for me to give out certain information but he's going to be out for a little bit of time so we'll have a chat with Lewis, we're talking with Everton now about where he's at and how's best to deal with that situation."