The 25-year-old has two years left on his current contract, but it is understood that the Demons will be open to trading their 3rd-string ruckman.
Preuss has played just 10 games across two season after battling an achilles injury, while playing reserve to Max Gawn and Luke Jackson at Melbourne.
The Giants have lost Sam Jacobs to retirement, while fellow tall Shane Mumford is set to join him in hanging top the boots, with afl.com.au reporting both NSW clubs will be chasing Preuss in the upcoming trade period.
Sydney lost starting ruckman Sam Naismith to a season-ending ACL injury in June and could be looking to add stability to their ruck stocks.
Preuss joined Melbourne on a four-year contract after leaving the Kangaroos in 2018.