The 22-year-old’s future has been the subject of speculation through the summer but suitors Tottenham only have until Thursday’s transfer deadline to prise him away from Villa Park.
Villa’s bargaining position has been significantly strengthened by the arrival of new majority shareholders Nassef Sawiris and Wes Edens, who have made clear they will not lower their valuation for the club’s star man.
Grealish played as Villa opened their Championship campaign with a 3-1 win at Hull last night and Bruce said: "He's a wonderful talent and we will do our best to keep him, but obviously it's going to be difficult.
"The human side of him wants to play in the Premier League, Europe, the Champions League - it's all natural.
"I'm sure it's going to be a fraught two or three days, but the owner has made it clear he wants him to stay and that's what we will try to do.
The boss continued: “They’ve made it clear they don’t want to sell him and that still stands. If they get to a magical figure, we’ll see.”
Tommy Elphick and Ahmed Elmohamady scored their first goals for the club, while Alan Hutton netted for the first time since December 2014 as Villa came from behind to win at Hull after Evandro had opened the scoring early for the hosts.
“It was an awful goal and when you give one of those away you think, uh-oh,” said Bruce.
“The second half we were a bit brighter in our work. We ran quicker and moved the ball quicker and showed a bit more purpose going forward.
“We are still way, way short of where we want to be. Yes it is nice to get off to a good start but we are under no illusions there is a lot of work to be done.”
Bruce, meanwhile, remained coy on whether Manchester City striker Lukas Nmecha is a target for his team.
The 19-year-old was pictured watching last night’s game from the KCOM Stadium director’s box.
Axel Tuanzebe became Villa’s second signing of the summer when he joined on a season-long loan from Manchester United on Monday.
Goalkeeper Orjan Nyland is expected to complete his move from FC Ingolstadt on Tuesday, while Villa have also had a bid accepted for Bristol City full-back Joe Bryan.
“We are close to one or two things,” said Bruce. “Hopefully we will get them over the line and be better than where we are at this particular moment.
“The plan forward is not just a sticking plaster. It is going to take time. Too often now we have just tried to make rash decisions and it has not paid off.”