Former Liverpool boss Houllier is set to take over at Villa Park as the club's new manager following Martin O'Neill's departure this summer.
Thompson worked with the Frenchman at Anfield, and it had been suggested the pair could be reunited at Premier League side Villa.
However, it is understood that Thompson will not be joining Houllier, who is currently France's technical director, at Villa Park.
The latest reports in France suggest that Houllier has agreed a two-year contract with Villa.
It is claimed he is set to meet French federation president Fernand Duchaussoy on Wednesday to discuss taking over at Villa.
Houllier will be only the second foreign coach to take charge of the Midlands club after Jozef Venglos' ill-fated spell two decades ago.
He is set to be named as the 25th manager in Villa's 126-year history and their fifth manager of the new millennium after John Gregory, Graham Taylor, David O'Leary and O'Neill.
It will represent the end of a six-year exile from the Premier League for Houllier since his reign at Liverpool came to an end in May 2004.
Houllier, who has been working as France's technical director, is expected to face the media for the first time in his new role on Thursday. His first match in charge would be the away clash with Stoke on Monday.
It is still to be decided what role the current caretaker boss Kevin MacDonald - an ex-Liverpool player - would have under the new regime.
He has been successful as reserve team coach but may be offered a post as part of the first-team set-up.