Adding to the club's frustrations since their disappointing 2022 campaign, star names in Nick Haynes and Lachie Whitfield have also been raised this week, while Greene's name is the latest to be included in the rumour mill.
Speaking on Wednesday night, 7 News' Tom Browne revealed, and quickly dashed, reports of rival clubs seeing Greene as an attainable asset in 2022 given he may be left "frustrated" by the ongoing list changes.
"Toby Greene's name came up today, the star Giant," Browne said.
"I think several clubs are of the view he's a bit frustrated that Hopper and Taranto have both gone, or will go, to the Tigers.
Key discussions are underway with a Giant name thrown into the mix. Chief Football Reporter @TomBrowne7 has the exclusive details. https://t.co/5zYfOfGqUb @7AFL #AFLTrades #InsideTrades pic.twitter.com/4sFO9nK83K
— 7NEWS Melbourne (@7NewsMelbourne) October 5, 2022
"He's got four years to run on a deal worth north of a million dollars a year, he's also the Giants' coveted co-captain."
Suggesting the reports came from those that may enjoy 'kite flying', Bartel gave a short answer in response to the rumours.
"No," Bartel said on 3AW.
"Let out the reel."
Greene is currently contracted to GWS until the end of 2026, while Haynes and Whitfield are also signed to the Giants until 2024 and 2027 respectively.
Kingsley will also welcome an array of young talent through the draft this year, with the Giants currently holding four picks in the top 20 selections for the 2022 National Draft.