Greater Western Sydney are believed to have double the terms originally tabled for the Bendigo product, moving from a two-year deal to four years.
St Kilda have been named as a hopeful suitor for Caldwell, while the Giants remain confident their onballer will stay in the Harbour City.
Caldwell was taken with the 11th overall selection in the 2018 Draft and has shown glimpses of star potential across his two seasons with the club.
The midfielder played nine games in 2020, averaging 12 disposals and 3.7 tackles per game.
Caldwell joins fellow first round Giants of the 2018 draft class in Jackson Hately and Xavier O’Halloran in remaining out of a contract for 2021.
Young defender Isaac Cumming is expected to sign a new deal with the club shortly.