It was announced on Tuesday that the Denver-based Kroenke, already Arsenal's largest individual shareholder, had increased his stake to 28.9 percent after buying 10 additional shares at a cost of some 85,000 pounds (138,712 dollars).
That followed his 765,000 pounds (1.249 million dollars) share purchase earlier this month and left Kroenke one percent short of the 29.9 percent mark which, under British company rules, would require him to launch a takeover of Arsenal.
At the London club's Annual General Meeting (AGM) last week, Kroenke remained silent when asked about his plans.
Gunners chairman Peter Hill-Wood intervened, pointing out that any public statements regarding future bid intentions must be unambiguous, otherwise the individual or group would, under the rules, be prevented from making a formal move for six months.