American businessman Kroenke, 69, who is worth £5.8bn, first bought a 9.9 per cent share in Arsenal in April 2007.
Russian billionaire Alisher Usmanov has once again returned to the Arsenal negotiating table, with reports indicating his desire to buy out current majority shareholder Stan Kroenke.
The Financial Times quotes a source as saying: "Two weeks ago, I thought something could realistically happen. Now I am not so sure", a person close to the situation said.
The men have been at odds for a number of years over the direction of the club.
Arsenal did not immediately respond to a request for comment.
While the pair have been at loggerheads for years, Usmanov is said to be "increasingly concerned" about the lack of investment being made in the club by "Silent Stan" and his board, from which the Uzbekistan steel magnate has been excluded. In an interview with Bloomberg last month, Usmanov said the blame for the club's performance should not rest exclusively with Wenger, but also with Kroenke and the board, from which Mr Usmanov is excluded.More news: Senate chairman: Flynn has not responded to subpoena
The takeover bid adds to the sense of uncertainty surrounding the club, with Arsene Wenger's future beyond this season still up in the air.
Mr Usmanov is not planning on disposing of his stake and the offer to buy out Mr Kroenke came from a desire to work co-operatively and strengthen the team, one of these people said.
It is Usmanov's latest move in a decade-long battle to own Arsenal, having built up a 30 percent stake in the Premier League club since 2007.
The 63-year-old now owns 30 per cent of the club through Red & White Holdings and has made a move to wrestle a further 67 per cent away from majority shareholder Stan Kroenke.
Also, a very big weekend in the Premier League for both Liverpool and Arsenal as they both look to capture the last qualification spot in next year's Champions League.
Arsenal Holdings made a pre-tax profit of 2.9 million pounds in 2016, on revenue of 353.5 million pounds ($461 million).