McLeish has revealed Grealish met representatives from Manchester United to discuss a move to the club all the way back in 2012.
Speaking on the Claret & Blue podcast McLeish said United's interest in the player began when he was just 16 years old.
"At that moment we felt people were getting in contact with him to leave Villa," he said. "That was one of the main reasons to get him involved with us (in the first team).
"He would have been on the bench anyway because of the casualties we had. He was the best youngster coming through.
"When we played Man United we heard he was in a restaurant being courted by one of the agents to try and get him to Man United.
"We were a bit alarmed about that so we fought well to keep him. We knew he loved Villa, his old man as well. We had them in speaking to them. They're lovely people.
"They asked for something and the club went it's too much but, finally, you come to an agreement and everybody's happy. Jack stayed at Aston Villa, which is great to see one of the great players of Villa nowadays staying with his boyhood club."