The Cats are firmly in the mix for both Greene and Butters, who has told the Power he wants to continue his career in his native Victoria.
Greene, the greatest player in the Giants' 15-year history, is considering making the same move so he has more support for his young family.
The 32-year-old recently met with the Cats to discuss what looms as the toughest decision of his decorated career.
"I've had a busy week and there's probably a fair bit of thinking coming up for next week - sort of really wrestling with the decision," Greene told SEN on Friday.
"It's something I'll work out with (wife) Georgia and the family over the next hopefully only a week or so.
"The factor to come home to Victoria would be (because of) family.
"If we want to have more kids, life's a bit easier, and that's something I've been open about. That's just the reality of the situation."
Greene said he had already discussed aspects of his possible on-field role with Geelong, while still feeling strongly about GWS.
"I love the Giants. I've put all my time and effort into that for 15 years and love the people there and love the club," Greene said.
"To have success there would be the best thing I could do in footy. That's sort of what I wrestle with at the moment.
"All the contracts are all pretty similar, (so) it's not really a factor in this decision."
A restricted free agent, three-time Port club champion Butters has attracted strong interest from Geelong, the Western Bulldogs and Richmond.
The 25-year-old is reportedly entertaining offers of up to $18 million over nine years.
"I asked (Geelong about Butters). It's important," Greene said.
"I spoke to Zak as well and it's something I will do again in the next few days. He adds a bit of weight to that decision.
"I wanted to see where his head was at (and) the things he values highly in his decision. That's what I asked him."
Greene and Butters loom as two of the biggest names that will shape the AFL trade and free agency periods, which start in October.
Zach Merrett is widely expected to again demand a trade away from Essendon, while key forward Ben King is set to leave Gold Coast.
Brownlow medallist Lachie Neale is poised to depart Brisbane, with Collingwood the most likely destination.
Lions veteran Dayne Zorko was unfazed by the speculation around Neale ahead of the qualifying final against Sydney, with Chris Fagan's men chasing a third straight premiership.
"He looks great in a lot of colours, but at the moment in maroon, blue and yellow, he looks just absolutely fine," Zorko told reporters on Friday.
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