Kroenke recently acquired ITV's 9.9 per cent Arsenal stake in a £60 million deal and has since taken his holding to 11.26 per cent.
Any takeover deal would place Kroenke at the end of a growing list of Americans that have bought their way into the Premiership. Ahead of him were Thomas Hicks and George Gillett, (Liverpool), Randy Lerner, (Aston Villa) and the trailblazer, Malcolm Glazer (Manchester United).
Dein was thought to be in favour of selling the club to Kroenke, but the other directors have no plans to sell their shares.
Arsenal chairman, Peter Hill-Wood, said there were "irreconcilable differences between Mr Dein and the rest of the board" that "necessitated a parting of the ways".
He also said that three other directors, Danny Fiszman, Lady Nina Bracewell-Smith and Richard Carr, who between them own more than 44 per cent of the club, had "no intention" of selling to Kroenke.
