Mr Kroenke also owns a number of US sports clubs
Arsenal director Stan Kroenke, the largest shareholder at the north London club, has increased his stake again.
Mr Kroenke has bought a further 80 shares at £8,500 per share, taking his holding in Arsenal to 28.7%.
It takes Mr Kroenke closer to the 29.9% threshold that would force him to make an offer for the remaining shares.
The American tycoon had been increasing his stake this year, giving him a bigger holding than Uzbek metals magnate Alisher Usmanov.
Mr Kroenke also owns the NBA's Denver Nuggets, the NHL's Colorado Avalanche, and the Colorado Rapids of Major League Soccer.
His latest move comes two days after Arsenal revealed its annual pre-tax profits had risen to £45.5m in the year to 31 May.
Mr Usmanov, a billionaire, owns more than 25% of the club through investment vehicle Red and White Holdings.