Grealish, 22, is believed to be keen on joining Mauricio Pochettino's side after a season in the Championship.
Spurs, though, are yet to meet Villa's valuation, with the Midlands club's financial strains eased by the arrival of fresh investment in July.
Bruce is confident of keeping Grealish beyond the end of the transfer window, but expects to face a fight for his services considering the stature of Tottenham.
"He is not for sale, however, it is very difficult when we are competing against a team which is one of the big teams in Europe now, not just in this country, and has played in the Champions League," Bruce told Sky Sports.
"But the owner has made it pretty clear that he does not want to sell anybody and that includes Jack."
Spurs boss Pochettino has consistently been thwarted in attempting to reinforce his squad, which could enter the new season without any off-season arrivals.
"We are working so hard but still we are like it's the first day of the transfer window – with no signings," the Argentine coach told a press conference.
"I think I am not the person to explain it.
"Of course, people expect the manager to explain that but, for different reasons, it's been difficult to add players who can help us. But in the last week many things can happen."