The talented Tiwi Islander sustained a hamstring injury in Melbourne's only NAB Cup clash against Hawthorn at Aurora Stadium on February 21.
But Wonaeamirri played in a practice match for VFL affiliate side Casey Scorpions last weekend and according to Melbourne football operations manager Craig Notman, 'Aussie' got through as expected.
"He showed a few signs that he won't be too far away," Notman told melbournefc.com.au.
But defender Daniel Bell remains out of action for up to a month with a broken thumb.
"He had an operation early last week to repair a broken thumb that he suffered in the last game against the Western Bulldogs," Notman said.
"He's looking at three or four weeks before he's back ready to go."
Ruckman Mark Jamar (foot stress fracture), on the long-term injury list, is still six to eight weeks away.
Jack Grimes (back) faces another three weeks on the sidelines, Matthew Whelan (calf) is out for a further two and Paul Wheatley (calf) is one match away from resuming.
Melbourne forward Russell Robertson, who has not played since round 10 last year due to a serious achilles injury, is also tracking well.
"It's been a long haul for him, so he's just about ready to go again," Notman said.
"He's been doing a fair bit of the work with the group now. It's been a long, drawn out process, but he's ticking all of the boxes with the medical staff and they're looking at two weeks, so he's done pretty well."
First-year Demon James Strauss will also miss two more weeks, after injuring his ankle while playing for Casey in a recent practice match.
