The 31-year-old left-back was at Leeds between 1995 and 2003 and made almost 300 appearances for the Whites before leaving for Spanish side Levante.
The former Republic of Ireland international returned to English football with Sunderland, but has been without a club since the summer after being released by the Black Cats.
Harte was given a surprise run-out for Leeds when he played in a behind- closed-doors game against Nottingham Forest on Tuesday.
Gary McAllister may be tempted to give Harte a short-term contract if he would be willing to play in League One.
With Alan Sheehan out injured Leeds have given a debut to young starlet Aidan White this season, while more recently Ben Parker has featured in the role after being given a run in the team.