In a brief statement to the London Stock Exchange on Monday, headlined "Response to media speculation", KSE said: "KSE UK Inc notes the recent media speculation concerning its shareholding in Arsenal Holdings PLC and confirms that its shares are not, and never have been, for sale."
It added: "KSE is a committed, long term investor in Arsenal and will remain so."
The statement came after last Friday's Financial Times reported that Russian billionaire Alisher Usmanov had made a $1.3 billion (£998 million, 1.1 billion euros) bid to take control of Arsenal from Kroenke.
Uzbekistan-born Usmanov owns 30 percent of Arsenal and is said to have recently made the offer in a letter to American sports entrepreneur Kroenke, who controls a 67 percent stake.
Usmanov, who made his fortune in the steel industry, had seen a previous bid for Arsenal rejected.
His criticism of Kroenke's passive ownership style was echoed by increasing numbers of Arsenal fans this season, who were unhappy with what they saw as the board's willingness to settle for on-field mediocrity so long as commercial stability was maintained.
Both 'Silent Stan', as Kroenke has been disparagingly nicknamed by some supporters, and Arsenal manager Arsene Wenger came under fire during a Premier League campaign that ended with the Gunners finishing fifth on Sunday.
That meant Arsenal missed out on a place in Europe's elite and highly lucrative Champions League for the first time in 20 years under veteran boss Wenger.
The 67-year-old Frenchman has faced repeated calls to quit and bring to an end an Arsenal reign that started in September 1996 when his current contract expires after the end of this season.
Wenger has yet to clarify his future but reports in the British press over the weekend suggested he would accept a new two-year contract.
Arsenal have one last chance to end the season with a trophy when they face Premier League champions and London rivals Chelsea in the FA Cup final at Wembley on Saturday.