Thompson received a letter from the club which cited his 'poor performance' as the main reason for him being disciplined.
The Daily Star reports that Thompspn has reported the club to the League Managers Association and asked them to take up his case.
Thompson has been suspended with immediate effect and told his contract will not be renewed in the summer.
Thompson only joined the coaching staff two months ago after leaving Huddersfield.
He quit the Terriers after being lured to Elland Road by Leeds coach Neil Redfearn.