Jack, who was a late withdrawal from the Swans’ round one match against GWS due to back soreness, took part in the majority of Tuesday’s training session at Lakeside Oval and moved freely throughout.
Club physiotherapist Matt Cameron said the co-captain would be fit to play if he gets through Thursday’s final session.
“He’s moving really well now and he’s joined skills training with the team,” Cameron told SwansTV’s HCF Injury Update.
“He pulled up with acute back pain on the morning of the game and it did take a few days to settle down.
“But he was able to run late last week pretty comfortably and he joined skills training today, so we’ll see how he copes with that.”
Lewis Roberts-Thomson will also face a test later this week after suffering a groin injury in the Swans’ season opener.
Cameron said his condition had improved over the last week, but Roberts-Thomson would still need to prove his fitness in Thursday’s training session.
“He jarred his hip joint but didn’t tear any muscles during the game and was unable to finish,” Cameron said.
“As the week has gone on, he’s just got better and better so he’s feeling good at the moment, but he hasn’t done any team training yet.
“He’s due to try that this week and we’ll see how he copes with it.”
Kurt Tippett is scheduled to resume skills training next week after a prolonged period on the sidelines with knee tendonitis.
The forward has stepped up the intensity of his fitness program this week, and ran laps at Tuesday’s training session.
“Kurt is running faster now,” Cameron said.
“He’s had some tendon pain in his knee, but he’s certainly running faster now.
“We’re hoping to have him skill training at the end of next week.”
Adam Goodes, who is recovering from a knee injury, is also making progress.
“We’ll build his speed next week and we’ll see how he copes with that in terms of skill training and will make a decision on that next week,” Cameron said.
Cameron also confirmed that Tommy Walsh, who suffered a severe hamstring tear in round 10 last season, would make his long-awaited return to training next week.
“Tommy has been working really hard in rehab over the summer to get his hamstring strong after tearing it off the bone in the middle of the year last year,” he said.
“We’re really quite happy with his strength now in his hammy and he’s been running faster and faster, and he’s due to start training next week.
“He starts in a phase now of skill training and then we’ll make a decision about his return to play.
In other injury news, young defender Alex Johnson underwent arthroscopic surgery on his left knee on Monday night and is expected to make a decision regarding his third knee reconstruction in the coming weeks.
