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6 year oldVichai 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.
One witness said he saw Leicester player Kasper Schmeichel run out of the stadium towards the scene of the crash.
It has not been confirmed how many other people were on the helicopter.
But a report by Reuters, which the BBC has not been able to verify, claimed four other people were on board with Mr Srivaddhanaprabha.
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.
Witnesses said they saw it just clear the stadium before it spiralled out of control, with some describing seeing a fireball as it crashed.
Under Mr Srivaddhanaprabha's ownership, the club won the Premier League in 2016, having started the season as 5,000/1 outsiders.
Season ticket-holder Richard Jackson, 53, from Market Bosworth, Leicestershire, travelled to the stadium to join with other fans.
"I'm just devastated really, it is such a tragedy you don't expect to happen," he said.
"These owners have been absolutely fantastic, probably the best owners in the whole English system."
Former Scotland winger Pat Nevin said the owners were popular with Leicester's supporters.
The football pundit said: "Whenever Leicester fans rang in to gripe about the team, they were never aimed at the owners."
Minute's silences were held ahead of the Premier League matches between Burnley and Chelsea, and Crystal Palace and Arsenal.
Leicester City said it was assisting police and emergency services and would issue a more detailed statement in due course.
By Samantha Fisher, BBC News
There has been a steady flow of people wearing Leicester City shirts and hats this morning.
Despite the number of fans gathered here it's very quiet.
Lots of children are also here with their parents laying flowers outside the ground.
Many people have been in tears as they approach the stadium and they've all been consoling each other.
Richard Mobbs, from Burton Overy in Leicestershire, said he last saw the chairman in June when they discussed a player who was about to join the club.
"I spoke to Vichai a lot," the 68-year-old said.
"It is such a shock. You just have to pay your respects."
Mr Mobbs described Mr Srivaddhanaprabha as a "lovely, quiet, down to earth man", and paid tribute to his family.
"They are all friendly," he said.
"This season they bought me a season ticket."
Anupat Maturongpituck, a student from Thailand studying at the University of Leicester, came to the King Power Stadium on Sunday to "pay my respects", adding news of the crash has had a "great impact" in Thailand.
Freelance photographer Ryan Brown, who was covering the game, saw the helicopter clear the King Power Stadium before it crashed.
He told BBC Radio Leicester: "The engine stopped and I turned round and it made a bit of a whirring noise, like a grinding noise.
"The helicopter just went silent, I turned round and it was just spinning, out of control. And then there was a big bang and then [a] big fireball."
Sky Sports News reporter Rob Dorsett said the helicopter took off from the pitch, as it does after every game.
He said that after a few seconds it appeared to lose control and crashed just a few hundred metres away.
'I have seen staff in tears' - Reaction to Leicester helicopter crash
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