'Dusty' has been the subject of persistent trade rumours, with some predicting an end-of-season Martin trade request to the Giants.
Speaking on Fox Footy's On the Couch on Monday evening, Greene detailed his stance on playing with Martin and a potential GWS pursuit of the superstar.
"It would be good. I'd love to play with Dusty," Greene said.
"I'm not too sure what's going on there and where his contract's at, but we'd be silly not to talk to him and I'm sure that'll happen if there is a chance of him potentially leaving."
Asked if he'd be willing to help persuade Martin to make the move to NSW, Greene was categorical.
"I would yeah, definitely. It'd be nothing better than to have him playing in the forward line or midfield next year," he said.
The 28-year-old was also questioned about the futures of Giants midfielders Tim Taranto, Jacob Hopper and Tanner Bruhn, as well as forward Bobby Hill, who are reportedly being circled by rival clubs and are departure candidates at the end of this season.
"There's obviously a lot of talk about [player movement] at the moment and there's probably some boys making some decisions in their head. That's up to them," Greene said.
"We really want to keep everyone we want at the footy club.
"We've obviously got a lot of good inside mids, but you can't have too many at the one time. It is what it is and we'll make the decisions based off that.
"I'm sure there'll be a bit happening in our off-season no doubt about it, but hopefully the powers that be can make the right decisions."
After providing a mark-of-the-year candidate in their loss to the Blues last weekend, Greene's Giants will go into battle against cross-town rivals Sydney this Saturday as they look to claim their sixth win of the season.