Leeds chairman Prof John McKenzie is believed to want a former Leeds player at the helm to keep the fans on his side.
Hart, after guiding the Reds to the playoffs last season, is clear favourite to take over at Elland Road with some bookies offering only 2/1.
Gordon Strachan is unlikely to leave Southampton but is available at 20/1 and Coventry player/manager and former Leeds captain Gary McAllister is a good bet at 10/1.
Meanwhile, Forest's Reid has been called up for Ireland's senior squad for the first time. They take on Denmark in a friendly next week and the skillful 21-year-old is delighted.
He said: "I'd love to win my first cap but just being a part of the senior squad is sure to be a great experience."