AFL.com.au understands the Giants have spoken to Thornton, 28, about joining the club for the 2013 season.
The unrestricted free agent told the Blues at the start of September he wanted out of the club, along with teammate Jordan Russell.
The Giants view the 188-game veteran as a good fit after losing the on-field experience of Luke Power and James McDonald at the end of the season.
Despite spending time as a forward during his career at Carlton, Thornton will likely fit straight into the Giants' inexperienced and undersized defence.
Thornton's manager, Anthony McConville, said at the start of the Gillette AFL Free Agency Period his client would happily move interstate to continue his career.
It is likely the Giants will wait until the free agency period closes on Friday before recruiting Thornton.
Trade Machine
Thornton managed just seven games with the Blues in 2012 after playing 20, including Carlton's two finals, in 2011.
His last game for the club came in round 18 of this year, when he had seven possessions in the Blues' win over Richmond at the MCG.
Trade tracker
The Giants are enjoying a solid off-season.
The club, under list manager Stephen Silvagni, has again performed a trade masterclass, already securing picks 1, 2, 3, 12 and 13 in the first round of the draft.
Meanwhile, a number of young Giants stars - including Jonathon Patton and Jeremy Cameron - are recovering well from post-season surgeries, with the club expecting a near full list ready to resume training in a few weeks.
Veteran ruckman Dean Brogan is still weighing whether to continue his AFL career, while the future of Jonathan Giles - who has attracted trade interest from Adelaide - is likely to be known soon.
While Thornton's future looks safe, two of his former Carlton teammates - Russell and Paul Bower - remain in footy limbo.
Russell's future is on hold after being told by new Port Adelaide coach Ken Hinkley he would not be recruited to Alberton, while Bower has been delisted by the Blues and will likely enter the draft.
