The club have spent big again in the transfer window as they look to push up the Premier League table after avoiding relegation by just a point last term.
Striker Ollie Watkins has joined from Brentford in a club record £28million deal while billionaire owners Nassef Sawiris and Wes Edens have a long-term aim of establishing Villa among the European elite.
But Grealish, who this week committed his future to the club by signing a new five-year deal, believes they need to be realistic over what can be achieved in the short-term.
“We haven’t sat down as a group yet but I am sure we will do that before the season starts and set out our goals,” he said.
“Everyone wants to build on what we have done last season. At the start of last year we were probably aiming to finish between 12th and 14th but it does not always work out as you plan.
“Hopefully we can build on that this season. With the squad we have I believe we can aim high.
“I think we have to be looking between 12th and eighth. You have to be realistic. You are not going to from finishing 17th one season and then going to fifth or sixth the next, as nice as that would be.
“I think if we could finish anywhere between eighth and 12th that would be brilliant.”
Grealish is also aiming to improve on a career-best season which saw him score 10 goals in all competitions and earned a first senior England call-up.
The 25-year-old made his Three Lions debut in a 0-0 draw against Denmark earlier this month.
He said: “As an attacking player you have to look at stats. I want to get goals and assist because if I do that I am doing my job.
“I obviously got into the England squad last month and that is a big thing. I want to get into more squads and become a regular for England because I genuinely believe I can.
“Making my debut was emotional. It was when I was putting my shirt on I was thinking: “As if? I’m about to play for England!’
“When you are sitting around with the rest of the squad it is weird. Sometimes you think you deserve to be there but sometimes you are thinking: ‘Wow, I’m in the England squad here.’
“It is something I want to build on and become a regular thing.”