Vichai Srivaddhanaprabha was in the helicopter when it came down at about 20:30 BST on Saturday, a source close to the family has told the BBC.
Witnesses said they saw it just clear the stadium before it spiralled out of control and crashed in a fireball.
The BBC understands two crew members and three passengers were on board.
Leicester had drawn 1-1 against West Ham United at the King Power Stadium, with the match finishing about one hour before the helicopter took off from the pitch.