Grealish, 25, is virtually certain to be in England's 26-man squad for Euro 2020 provided he can prove his fitness, after producing outstanding displays in his first senior appearances last autumn.
"Jack trained on Saturday and Tuesday and he trained very well," said Villa manager Smith.
"I'll have a chat with him and see he's got no ill effects.
"We'll sit down with the doctor as well and take it from there.
"Is he ready to start games? No, but if he feels pain-free then he's ready to be a part of the squad."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!