Grealish has been one of the Premier League’s standout players this season, despite Villa’s struggles, and also helped his boyhood club reach the EFL Cup final, where they lost to Manchester City.
That form has made the 24-year-old a summer target for United as Ole Gunnar Solskjaer looks to bolster his attacking options.
Things could have been different, however, had United’s first attempt eight years ago – when Grealish was a 16-year-old yet to make his senior debut – been successful.
“At that moment we felt people were getting in contact with him to leave Villa,” McLeish told the Claret and Blue Podcast.
“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.”