Greene, the greatest player in the Giants' 15-year history, is heavily considering finishing his career back in Victoria so he has more support for his young family.
Admitting it will be the toughest decision of his career, the 32-year-old denied he had already made up his mind about leaving GWS.
"I felt like a lot of people in Melbourne, or friends, maybe even some people at the club, feel like I'm definitely going, which is not true," Greene told the Ausmerican Aces podcast.
"If I was definitely going, I'd say that now. I'd be up-front with the Giants and make it easy for them."
Greene's good friend and former GWS teammate Jeremy Cameron looms as a natural attraction at Geelong.
Wooden spooners Essendon are desperate for senior stars to help their young talent develop.
Former Giants assistant Mark McVeigh has just been appointed Bombers coach and wants to talk with Greene.
"I'll meet with Geelong probably this weekend, I'd say," he said.
"I couldn't give a f*** about the tour, to be honest. I couldn't care about what their footy club looks like. They're a bloody good club.
"I'd do weights at Anytime Fitness, if I have to.
"'Spike' (McVeigh) has reached out as well since he got the job and asked to catch up.
"I said I'd catch up with him, but it wasn't exactly what I was thinking all year at all."
GWS missed finals for the first time since 2022, with several experienced players already making an exit.
Coleman medallist Jesse Hogan, enigmatic forward Jake Stringer and ruckman Kieren Briggs are confirmed departures.
"If I didn't think the Giants would finish top-four next year, I wouldn't stay," Greene said.
"One thing I want to do with them is win a flag and that's the best thing I could do ever in footy.
"I could win two or three (premierships) somewhere else, it wouldn't be as good as one at the Giants."
Greene has played 282 games for the GWS after playing in the club's first AFL game back in 2012.
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