The boss confirmed Grealish will be assessed on a game-by-game basis for an injury sustained in training last week.
Speaking after Villa’s 2-1 defeat to the Foxes, boss Smith explained: “On Friday Jack had some discomfort so we pulled him out of training and assessed him. We didn’t think he was right for the game.
“It is not a reoccurrence of a longstanding injury or an old injury and it is not going to be a long-term injury.
“But I am guided by the medical staff to how long he will be out. It is pretty much game-to-game.
“We are hoping he could be back for Leeds and if not Sheffield United but I have to be guided by Jack and the medical staff. They will keep assessing him and see how he is.”
Smith also vowed to investigate after rumours of Grealish’s injury leaked online in the hours before kick-off.
Leicester boss Brendan Rodgers later confirmed his team had been aware Villa’s skipper might be sidelined.
Smith said: “I was made aware that on social media there were rumours he (Grealish) was not going to play.
“If that is coming out of our training ground I will find out where it is coming from and reprimand whoever it is coming from.
“It certainly does (give the opposition a leg up). It is something I would not be happy with and we will get to the bottom of it.”