Swallow ruptured his left Achilles tendon against Melbourne in round 18 last season, with Petrie standing in as captain since then.
Petrie told the AFL Exchange podcast on Wednesday that Swallow's return date remained "a week-by-week proposition", but said his progress on the training track was encouraging.
"He's running, he's kicking the footy, he's doing some agility work, so he's not too far away," Petrie said.
"He's going at about 60-70 per cent."
Petrie said Swallow's next step would be to test his Achilles with more explosive training.
"It's acceleration and it's the agility movements, which is basically his in-and-under ball-winning ability and then having to sprint off," Petrie said.
"It's (doing) those movements that he needs to have confidence in the Achilles before he gets going again."
At North Melbourne training on Thursday, Swallow moved well as he completed a series of three-quarter pace run-throughs.
Twitter: @AFL_Nick.
