Knowing off-contract Greene and his Geelong home well, Idun finds the idea of his captain leaving sunny Sydney simply "funny".
The Cats have emerged as a possible suitor for the 32-year-old Greene, who has played all 270 games in his career at GWS.
An inaugural Giant, Greene in April surpassed Callan Ward as the club's all-time games record holder when he played his 268th game.
Describing the Giants skipper as the "most loyal bloke I've ever met", vice-captain and Geelong-raised Idun had simple advice for Greene if he was contemplating a move.
"Check the weather," Idun said on Tuesday.
"He won't go back, no way.
"He's into his spearfishing at the moment, so he'll need a three-layer wetsuit if he goes down there.
"I don't think he'll like it."
Greene wouldn't be the first captain to seek a transfer after former West Coast skipper Oscar Allen (Brisbane) and St Kilda's Jack Steele (Melbourne) made moves last year.
Ex-skippers Zach Merrett (Essendon) and Jy Simpkin (North Melbourne) failed in their bids.
Greene, before his milestone 268th game, had mused about ending his career as a one-club player.
The crafty forward has taken the Giants to new heights since taking over as stand-alone captain in 2023, being named as All-Australian captain that year.
"I do find it funny, especially the 'Tubs' one - most loyal bloke I've ever met," Idun said.
"He hasn't spoken about it at the club, and no one will ask him, but we love the service he's provided.
"He's our captain, and we all love him."
Key forward Jesse Hogan's deal also runs out this year, alongside inaugural Giants player Stephen Coniglio and ruckman Kieren Briggs.
"Apart from seeing it on social media, like about Toby and Jesse, I wouldn't know who's out of contract," Idun said.
"We handle it pretty well. Just focus on week by week, as cliche as that is."
Hogan is expected to return for the club's away clash against West Coast after missing out on a 14-point comeback win against Essendon with a corked hip.
Trailing by 26 points during the third quarter, Idun embodied the club's 'never say die' attitude with a game-saving smother to deny a certain goal from Bombers youngster Jayden Nguyen in the final quarter.
"(I've watched it) a couple of times, yeah. Maybe about 50, if I'm honest," Idun joked.
"We know it's sort of getting a little bit desperate. If we lost on the weekend, it would make the season look pretty tough.
"The next three weeks (before the round-13 bye) are going to set us up for hopefully where we want to be in the finals."
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