The 25-year-old is the subject of serious interest from Premier League champions Manchester City who have been linked with a £100million swoop.
But Villa are determined to keep their most prized asset and last month opened talks with Grealish’s representatives over a new deal.
The club have already broken their transfer record this summer with the £33m signing of Emi Buendia and former striker Thompson believes keeping Grealish would be a further show of their lofty ambitions.
He told the Express & Star: “They have already shown intent by signing Buendia for big money and then pursuing Emile Smith Rowe at Arsenal.
“But keeping Grealish, considering the profile he has now and how heavily he has been linked with Man City, would be a big statement.”
Villa have been given an allocation of 2,232 for their Premier League opener at Watford on August 14.