Despite having four years to run on his contract with Carlton, the dual Coleman medallist is desperate to leave Ikon Park.
The Cats are Curnow's first choice and Geelong tabled their first-round picks for this year, as well as 2026 and 2027, in an attempt to lure Curnow to GMHBA Stadium.
But with the Cats coming off a losing grand final and expected to remain in premiership contention, their draft picks won't be attractive to Carlton.
"The club's position has been that we don't want Charlie to be leaving Carlton," new Blues football boss Chris Davies told Trade Radio on Friday.
"The second part of this conversation is understanding what three first-round picks might actually look like and, for Geelong, those three picks are effectively going to be picks in the 20s.
"If that's what the offer ends up being ... I'm not sure anyone would think that's a reasonable deal for who Charlie Curnow is.
"We value him far more than what some other people are suggesting around the competition he's worth."
Cats counterpart Andrew Mackie confirmed Carlton had knocked back the deal.
"It was the best offer that we could do," Mackie told Trade Radio.
"They're our three first-round picks.
"... Clearly the mechanism is now there to be able to trade three first-rounders.
"We wouldn't be doing it for everyone, but for this one we were willing to do it, and from our end it's as much as we could offer (for) a player of that age and where Charlie is."
Mackie said no Cats players had indicated they wanted a trade.
Sydney are better placed to trade for Curnow, who is more than open to joining the Swans if he can't get to Geelong.
The Swans are considering whether to package forward Will Hayward, or midfielder James Rowbottom, with a range of picks to better satisfy the Blues.
It has been a busy trade period for Carlton, who on Friday secured Gold Coast forward Ben Ainsworth and West Coast winger Campbell Chesser through separate trades.
As part of the Ainsworth deal, Blues small forward Corey Durdin has moved to Port Adelaide, with both clubs swapping several picks.
Port remain adamant they will not entertain any offers for star Zak Butters.
Carlton gave up a second-round draft pick (currently No.41) to lure Chesser.Â
Geelong are also trying to bring in contracted St Kilda ruckman Rowan Marshall, who is seeking a move due to the Saints recruiting Tom De Koning.
But the Saints are standing firm on the Cats' advances for Marshall, believing he and De Koning can work together as a ruck combination.
Geelong have re-signed veteran ruck Rhys Stanley in a sign their bid for Marshall could fail.
Meanwhile, Davies has suggested Carlton could pay out the final year of troubled utility Elijah Hollands' contract.
The Blues have told Hollands, whose brother Ollie is a regular at Carlton, to explore his options after taking personal leave on two occasions this year.
But there has been little interest in the former first-round draft pick, who moved to Carlton from Gold Coast at the end of 2023.
GWS will begin negotiations with Melbourne about Clayton Oliver after the Demons premiership midfielder's desire to be traded to the Giants.
New Melbourne coach Steven King told the contracted Oliver to seek opportunities elsewhere during a recent meeting.
Fellow Demons star Christian Petracca is also leaving, opting to join semi-finalists Gold Coast.
Collingwood premiership forward Brody Mihocek's move to Melbourne is official, with a deal confirmed on Friday.
