Green used his welcome speech at Friday night's club best-and-fairest function to shut down rampant speculation about the playing future of Oliver, who attended the dinner.
It is the second straight year that trade talk around Oliver has been a major issue ahead of the club's best-and-fairest function.
Green said he was looking forward to round one next season, when the Demons' midfield would feature captain Max Gawn, Jack Viney, Christian Petracca - and Oliver.
"I know, come round one next year, when I see the first ball bounced and our midfield of Gawn, Viney, Oliver and Petracca ... that you Melbourne faithful will be there in full force," Green said.
The mention of Oliver's name was met with applause.
The silly season officially started on Friday, with St Kilda defender Josh Battle joining Hawthorn via free agency.
Also on the move are Harry Perryman, who linked up with Collingwood from GWS, while Elliott Himmelberg joined Gold Coast from Adelaide.
The trade period itself begins on Monday.
Oliver met with Geelong this week as he considers his future, despite having six years left on a lucrative contract that runs until the end of 2030.
"My job is to put my arm around Clayton throughout this whole process," Demons captain Gawn had told Triple M earlier on Friday.
"I love Clayton the player, and I've told him that, but I love Clayton the person a whole lot more.
"I'm going to be there no matter what, throughout anything good or bad, and I hope Clayton knows that.
"Sometimes you can think your captain is sort of involved in a few things, I promise I'm not.
Melbourne had reportedly attempted to shop the midfielder around, prompting four-time best-and-fairest winner Oliver to test the market.
Clayton Oliver will be lining up for the Demons again next season.
The meeting with the Cats was said to have been held at ruckman Rhys Stanley's farm, with defender Tom Stewart and Geelong officials also on hand.
At Geelong's best-and-fairest on Thursday night, Stewart confirmed the meeting with 27-year-old Oliver.
"It was good. Obviously any sort of talent we can attract to the club is important for us," Stewart told the Seven Network.
"So I had the opportunity to meet with him and it's an interesting thing for me in my stage of the career, but it went well, he's a good man.
"It's not really pitching anything, it's just sort of enlightening him as to what we're about at the footy club and the things that we hold dear and the things that we really value.''
Geelong's top trade target is Western Bulldogs star Bailey Smith. (Joel Carrett/AAP PHOTOS)
Geelong would have needed to be creative in terms of trying to recruit Oliver, given their first-round draft pick will likely be used to obtain Western Bulldogs midfielder Bailey Smith.
Last year, chief executive Gary Pert released a statement via a letter to members just hours before the event, saying Oliver would not be traded.
The supremely gifted midfielder has struggled with his fitness and off-field issues over the past two years.
Coach Simon Goodwin has made it clear he wants to keep both Oliver and Petracca, who committed to the Demons for 2025 after agitating for a trade.
The unrest once again flies in the face of comments from Pert late last year that Melbourne's culture was the best he had seen in 40 years.
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