He is widely expected to retire in six months' time after more than 500 senior appearances for Leeds, but the defender turned 32 in July.
Drogheda are four points off the top of the Irish Premier Division, and boss Paul Doolin is hoping the offer of a competitive spell in the eircom League will persuade Kelly to delay his professional retirement.
Doolin said in the YEP: "I know it's Gary's last year over there, and that he has told people he is coming home. He may be 32 years old but he is certainly fit. He was in the Championship team of the year last season.
"If he is coming home then of course we would be interested."