Throughout the campaign, Grealish has been heavily linked with a future transfer to a bigger club, potentially Manchester United, who are said to be keen on the playmaker.
However, despite acknowledging that the Englishman would like to play in the Champions League, Barnett has reiterated that the 24-year-old's current priority is to help his boyhood club stay in England's top flight.
Speaking to Stretty News, Barnett said: "Jack believes it, he's fighting hard, as hard as he can to stop that. That's all that is on his mind at the moment. He's not interested in anything else other than fighting to get Aston Villa out of any trouble.
"On the other hand, I think as far as his career is concerned, it would be great for him to play in the Champions League and develop his great skills and I'm not sure in which country or where that will be.
"But that conversation won't happen now because all he wants to do is fight and help Aston Villa."
Ahead of facing United on Thursday night, Grealish has not contributed a goal or assist in his last seven Premier League appearances.