The 32-year-old has been with the Gunners since 2014 but has never been able to establish himself as a first-team regular under Arsene Wenger.
The France international has made only 13 Premier League appearances for the north Londoners and it seems he is surplus to requirements at the Emirates Stadium.
Debuchy appears to be in limbo and has not played a single minute for the club this season after just one top-flight appearance last term.
The former Newcastle defender will be out of contract next summer and confessed to L’Equipe that his future is uncertain after missing out on the Seagulls.
“I don’t know what will happen because this summer the coach would have let me leave without a transfer fee,” he said. “Brighton also enquired in the last few days of the transfer window. But that came to nothing.”
Hamilton manager Martin Canning is happy to have some selection dilemmas after coming through a major turnaround of his squad.