Shaw’s future at the Magpies was placed in doubt shortly after the side’s loss to Port Adelaide in week one of the finals and he was notably absent from the club’s best and fairest count on October 4.
On Monday night, GWS posted a statement on its website suggesting Shaw wanted to join older brother Rhyce in Sydney.
“A number of other clubs were chasing Heath so for him to say he wants to join the Giants is a great endorsement of the club and the direction we are taking,” GWS coach Leon Cameron said in the statement.
“Heath is exactly the sort of player we are looking for. He is a quality player who has enjoyed premiership success and will provide tremendous leadership for our young playing group.”
Collingwood confirmed on its Twitter account the club would be working with the Giants to ensure a deal is done for Shaw, who is contracted to the Magpies until the end of 2015, before the trade period ends on October 24.
GWS young gun Taylor Adams wants to return to his home state of Victoria and is likely to be involved in the Shaw deal.
Shaw, 27, played 173 games for Collingwood over nine seasons, and was part of the 2010 premiership side.
Rhyce Shaw, 31, reignited his AFL career when he left Collingwood at the end of the 2008 season to join the Swans.
News Corp reported Shaw’s deal with GWS would be for five years and worth between $675,000 and $700,000 a season.
Last week, the Giants denied reports they had dangled a $4 million ($800,000 a season) carrot in front of Shaw.
“The claim that we have made a $4 million offer is a wild exaggeration and simply wrong,” Giants football manager Graeme Allan said in a statement.