Swallow was hurt late in the Kangaroos' 54-point win over the Western Bulldogs on Saturday when opponent Dylan Addison fell across his leg.
The club's director of medical services Steve Saunders said the 25-year-old would complete only light duties this week, but had progressed well in his recovery so far.
"Andrew has presented very well today," Saunders told NMFC.com.au on Monday.
"He had his scan this afternoon and all the major ligaments look really good and sound.
"He has very little swelling and a high level of function, [so he] is a very good chance to be cleared to be available to play this week."
Saunders said the club was also "hopeful" NAB AFL Rising Star nominee Aaron Mullett would be fit to face the Eagles after being subbed out against the Bulldogs with a left ankle sprain.
"He'll be heavily modified for the next couple of days and we'll give him a test on Thursday, but he's tracking well," Saunders said.
Fellow defender Nathan Grima should return to the line-up after missing Saturday's win with soreness, but the news isn't as positive for Robbie Tarrant.
The key forward has already spent a month out with a lower leg injury, and faces up to three weeks more on the sidelines.
"Robbie had a contusion to the lower leg that's caused a neuropraxia, which is a badly bruised nerve," Saunders said.
"When you bruise a nerve it can take time because they are slow to heal.
"It's probably going to be another two to three weeks before he's available to play."
