Devon Smith has reportedly nominated Essendon as his club of choice, according to Fox Footy's Jake Niall.
The Bombers have beaten Carlton, Collingwood and St Kilda in the race to sign the wantaway GWS forward.
The report suggests discussions between the Giants and Bombers are yet to begin.
Smith expressed his interest in seeking a trade last week, alongside fellow Giants Matt Kennedy and Nathan Wilson.
Kennedy has nominated Carlton as his preferred destination, while Wilson, who wants to head home to Western Australia, wants to join Fremantle.
The 24-year-old played just 16 games this season after battling knee problems, kicking 15 goals.
He was left out of GWS's side for their preliminary final against Richmond, being named as an emergency.
He has played 109 games for the Giants across six seasons, kicking 100 goals.