"At the moment, Spurs haven't got anywhere near what the owners want to even consider, so there's not a discussion to be had," Bruce told a news conference on Friday.
"I don't think we've had a formal bid. The one thing that the owners have made pretty clear is no one is for sale. We don't want to lose our best players."
Villa lost the Championship playoff final against Fulham in May and their financial difficulties have since come to light.
However, they received a significant investment from NSWE, a company jointly owned by billionaires Nassef Sawiris and Wes Edens, in July and are under no pressure to sell their prized asset.
Grealish, who joined Villa as a trainee in 2011, has become a vital part of the team with his energy and drive. The 22-year-old has Premier League experience too, having played 34 times in the top flight for the club.
Bruce said Tottenham would have to pay a premium to get their man before the transfer window closes on Aug. 9.
"The owners are aware that every player has got his price. The good thing they have been able to do is not let anybody go on the cheap. So if somebody wants to come and buy one of our players then they are going to have to find a premium and make sure that the owners are comfortable with that."
Tottenham are looking to improve on their third-placed finish last season. The ambitious club will move into a new stadium in the new season.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Mark Heinrich)
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