Giles, 26, is contracted at GWS to the end of next season, but the ruckman told the club in his post-season review that he was keen to find a new football home after being overlooked for senior selection in the second half of 2014.
AFL.com.au understands the Giants are sympathetic to Giles' situation and are prepared to work with him to try and broker a suitable trade.
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Reports have already linked the former Central District player with Port Adelaide, where Giles spent four seasons without playing a senior game, and Adelaide.
Giles is open to a return to the Power despite his unsuccessful first stint there.
However, the ruckman is by no means actively seeking a return to South Australia and is prepared to relocate anywhere to reignite his career.
It is understood Giles and his manager, Adrian Battiston of Stride Sports Management, have already received interest from some Victorian clubs.
As first revealed on AFL.com.au, defender Sam Frost and key-position player Kristian Jaksch are also planning to leave the Giants. Those two players have asked to return to their home state.
But if the Giants can't find a suitable trade for Giles, the ruckman is happy to serve out the remaining year of his contract.
Giles is a ready-made AFL ruckman who is sure to appeal to clubs in need of talls, especially given his proven ability to hit the scoreboard when pinch-hitting in attack.
Jonathan Giles battles with Swans ruckman Tom Derickx earlier this season. Picture: AFL Media
Giles made his AFL debut in the Giants' inaugural AFL game in round one, 2012, and became the first player to reach 50 games for the expansion club in round eight this year.
But after playing the Giants' first nine games this season, Giles was dropped and could not break back into the senior team despite outstanding form in the NEAFL.
Giles finished fifth in the Giants' 2012 best and fairest count, averaging 14.3 possessions and 22.1 hit-outs a game, and kicked 18 goals for the season.
He followed that up with a sixth-place finish in last year's best and fairest award, having not missed a game. Giles averaged 10.5 possessions and 24.3 hitouts a match in 2013 and kicked 14 goals.