The Villa boss told Sky Sports that Spurs' latest valuation, reportedly around £20m, isn't close to theirs, meaning the London side will have to act fast if they are to complete the deal before the Premier League transfer deadline on August 9 - especially with Chelsea reportedly waiting in the wings.
Spurs seemed to be closing in on completing the deal, but Bruce believes Villa haven't even received a proper offer, saying: "I don't think we've had a formal bid. There's been discussions and that's been going on all summer. The one thing the owners have made pretty clear is that no-one is for sale.
"We don't want to lose our best players, but they're aware of course that everyone has their price. The best thing the owners have been able to do is not let anybody go on the cheap.
"So if someone wants to buy our players, they're going to have to find a premium and make sure the owners are comfortable with it.
"We all know what football is, but at the moment Spurs haven't got anywhere near what the owners want to consider - so there's not a discussion to be had at the moment, because they've not got anywhere near the figure they demand."
The high profile interest in Grealish makes sense on the face of it. He's one of the most highly rated players outwith the Premier League, and has played a lot of senior football - almost 150 appearances for Aston Villa and Notts County - at just 22 years of age.
Despite missing the first 15 games of the Championship last season, his return to the side coincided with a drastic up turn in form which saw the Villains make the playoff final, before eventually losing out to Fulham.
Grealish's performance even in that Wembley defeat were enough to turn heads, possibly acting as the catalyst for Spurs' prolonged and unwavering interest in the Villa youth academy graduate.
Spurs, meanwhile, may view Josh Onomah - who spent last season on loan with Aston Villa - as an alternative to Grealish, as they are reportedly considering keeping him around as a first team option, rather than loaning him out.