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 Max Gawn told Triple M.
"I love Clayton the player, and I've told him that, but I love the 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.
"I don't sit in list management and I don't want to."
Melbourne had reportedly attempted to shop the midfielder around, prompting four-time best and fairest winner Oliver to test the market.
The meeting with the Cats was reportedly 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 Oliver, 27.
"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.
"There's a lot of things that need to happen if a potential deal gets done but if we can attract talent to the club, that's what we're about."
Any deal would likely require Melbourne to still pay part of Oliver's hefty salary.
Geelong will have to be smart in the market as they are also eyeing Western Bulldog Bailey Smith. (Joel Carrett/AAP PHOTOS)
Geelong would need to get creative in terms of trade capital, given their first-round draft pick will likely be used to obtain Western Bulldogs midfielder Bailey Smith.
Melbourne's best and fairest is on Friday night.
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.
That could happen again.
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 Christian 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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