The 25-year-old was due to come out of contract at the end of next season, but recently re-signed on a six-year contract extension, which ties him to the Blues until the end of 2029.
"There were some stupid big offers that came already for Charlie Curnow ahead of his free agency trigger year next year, an astronomical offer in particular from a rival club that stretched to seven years at more than $1 million a season over that tenure," Edmund told SEN.
"So the offers were coming thick and fast for him, as they’re for a lot of players at the moment."
The spearhead had spent a significant period out of the game due to various injuries, managing only four games over the 2020 and 2021 seasons.
But under new coach Michael Voss, Curnow has been able to recapture his best form and stormed home to win the 2022 Coleman Medal, kicking 64 goals, beating Richmond forward Tom Lynch by just the four majors.
The Blues forward was also named in the All-Australian team for the first time, capping off a fantastic season.
Carlton have now had back-to-back Coleman Medal winners, with Harry Mckay claiming the honour last season.
Mckay is due to reach free agent status next year, with Edmund noting that his signature is also a priority and will be "the next one they need to get done at Carlton.”
Carlton's season ended in heartbreaking fashion with a one-point loss to arch-rivals Collingwood in the last round of the season.