Stan Kroenke kept quiet at Arsenal's Annual General Meeting (AGM) on Thursday as Gunners officials refused to discuss the American billionaire investor's plans for the club.
Kroenke is now the largest individual shareholder in the Premier League side's holding company, with a stake of 28.86 percent.
Should Kroenke or the likes of Alisher Usmanov, the Russian industrialist who has the second largest stake in Arsenal, reach the 29.9 percent threshold that would trigger a formal takeover offer for the remainder of the club.
Kroenke remained silent when the question of his future involvement with Arsenal was raised at the AGM, with the London club's chairman Peter Hill-Wood saying: "I don't think we are looking for a change in custodian.
"I think you will find the club is in pretty good hands.
"I believe he (Kroenke) is happy to be a long-term shareholder in our club.
"Really its not for me to say what his intentions are."
The group headed by Kroenke, the owner of the Denver Nuggets basketball team, is just 646 shares short of the takeover threshold.
But any public statement must be unambiguous, otherwise the individual or group would, under the rules of England's takeover panel, be barred from making a bid for the remaining shares for six months.
Hill-Wood added: "It is not something I can discuss publicly or even privately. We have a takeover panel breathing down our necks and I have to be very careful with what I say."
Meanwhile, manager Arsene Wenger, who celebrated his 60th birthday on Thursday, was confident about the prospects for his youthful side, which are currently fourth in the table, four points behind leaders Manchester United and with a game in hand.
"I know that we haven't won a trophy for four years but we were very close," the Frenchman said. "I believe that this year the team will do it.
"When I say that, it is not to please you, it is because I am really convinced of it."