The Turf Moor club are understood to be interested in signing Douglas, who is entering the final year of his contract at Elland Road.
Douglas also appears to be out of the first team picture at Leeds as he was only a second half substitute on Saturday against Dender and Gary McAllister is set to name a new skipper this week for the season ahead.
McAllister needs to free up funds for new players, with striker Dougie Freedman and defender Paul Telfer on his wish-list.