A free agent since leaving West Ham last summer, Antonio had been training with Leicester City before Christmas before an injury setback saw any chance of landing contract fall through.
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Antonio, however, has been in talks with Charlton Athletic, though is also in contact with Qatar's Al‑Sailiya.
On the weekend, Addicks boss Nathan Jones said there was "nothing yet" to announce, but added that "the wheels are still in motion".
Talks with both clubs and Antonio's agents will continue today.
The Jamaica international, 35, has fully recovered from a serious car accident in December 24, which left him with a serious leg fracture.