Thompson was due to arrive in Yorkshire for talks with Leeds today after productive discussions between his representative Tony McGill and Ken Bates, with the Whites being given first opportunity to capture the Celtic midfielder.
Leeds are one of a group of clubs with an interest in Thompson, and at least one Premiership manager is waiting if the 33-year-old fails to reach agreement with Dennis Wise.
But United have taken the initiative by striking a deal with Celtic, and his remaining options have been put on hold while negotiations continue with Leeds.
McGill met with Bates yesterday and was flying into England today to accompany Thompson to Leeds.
He said: "The chairman made it very clear that Dennis Wise rates Alan. They want to sign him. There's competition from other clubs, and a Premiership club is interested, but we're not talking to anyone else at this moment in time.
"We won't think about doing so until talks with Leeds are concluded."
Asked if a move to Elland Road was Thompson's preferred option, McGill said: "It's looking that way. Leeds are in a difficult position but they've got good players there, and both Alan and myself have had a long look at the squad. We've been impressed with what we've seen.
"At this stage we've only been given permission to speak to Leeds, and talks are progressing."
United will attempt to sign Thompson until the end of the season, although McGill refused to confirm whether discussions were aimed at a loan deal or a permanent transfer.
The Newcastle-born player was signed from Aston Villa for £2.75m by Martin O'Neill in September 2000, and Celtic completed the domestic treble at the end of his first season in Scotland.
Thompson went on to make more than 150 league appearances and featured in the UEFA Cup final in 2003, but he last appeared in a Celtic shirt during their 2-2 draw at Aberdeen on the final day of last season.