Green suffered the setback in Melbourne's only win of the season so far, against Richmond in round four. Initially, he was expected to miss up to six weeks.
Melbourne coach Dean Bailey all but confirmed Green would return when he spoke to the media on Wednesday at the Junction Oval.
"He's one of our elite players, so I'm sure Brad will be playing on the weekend," Bailey said.
A handful of Demons are also in the mix to return, including impressive first-year running defender Jamie Bennell, who was rested last Saturday against the Western Bulldogs.
Bennell played his best match against the West Coast Eagles in round seven.
"He was 20 per cent soreness and 80 per cent rested," Bailey said.
Young players such as Bennell and Neville Jetta had to be managed carefully.
"They've done a good pre-season … but not as much as the other group, so our management loads on them are super important.
"It was important Jamie got rested last week, so he'll certainly be in the mix this week."
Tall defenders James Frawley (hip flexor) and Jared Rivers (ankle) are also a chance to resume after missing last round.
"They need to get through training tomorrow (Thursday). There is still a little bit of doubt on them, but they aren't looking too bad," Bailey said of the duo.
The Demons may also consider the versatile Tom McNamara, who has yet to debut, but keeps impressing with Casey Scorpions.
"Tommy Mac has been good the last couple of weeks at Casey and he went forward on the weekend and kicked two goals," Bailey said.
"It was really pleasing to see and he adds some flexibility to us.
"It's good to see him playing well and I'd like to play him. It might not be this week, but if his form keeps going, it'd be good to see Tom."
Ruckmen Mark Jamar and Jake Spencer are also not far away from a senior call-up, with the pair suffering recent foot injuries.
"The big 'Russian' Jamar was good on the weekend, playing at Casey and [Jake] Spencer is another one where we pulled heavily back on his training and playing for a week or so," Bailey said.
"He played a reserves game last week, so he'll certainly play at Casey again on the weekend.
"Jamar is certainly well advanced … his ruck work was good on the weekend, so he'll be a couple of weeks, maybe one [more] before we seriously look at him, but Spencer is at least one or two [more weeks away]."
Looking ahead to the Hawks, Bailey was encouraged by his side's recent form, but hoped a win was just around the corner.
"If we can keep our attitude right and start well and as long as we're in the game for as long as we can be, then you never know, it might come down to that last minute or that last two minutes," he said.
"That would be a great result for us – to be competitive with last year's premiers. It's going to be a great challenge and one that we want to get into on Sunday.
"You only need to turn the clock back 12 months, and I'd rather be in this situation than last year. We're moving forward and the players are getting close [to a win].
