The 32-year-old's agent admitted today that he was speaking to "a number of clubs", and Thompson could be tempted by the offer of a loan deal at Elland Road having failed to appear once for Celtic this season.
Thompson's agent, Tony McGill, refused to confirm United's interest, but said: "I'm talking to a number of clubs. It wouldn't be fair to discuss the situation further."
Leeds are also believed to be interested in Oldham winger Chris Taylor, who is enjoying an outstanding season with the League One club.
Taylor, 20 next week, has helped John Sheridan's side edge into the play-off zone with a series of quality performances, and Dennis Wise is one of several managers who are understood to be following the his progress.