But Jonathan Barnett has categorically denied any deal has been agreed for Grealish to move to Old Trafford.
"Absolutely no deal has been done with anybody," Barnett told Stretty News when asked about the reports.
Barnett also said that Grealish was confident Villa could avoid relegation, but added that it would be great for the midfielder to play in the Champions League in the future.
"I don't think they're [Aston Villa] looking at the Championship themselves, they believe that hopefully they'll get out of the trouble they're in.
"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."