Stan Kroenke has purchased another 427 shares in Arsenal's parent holding company, raising his stake to 29.6 per cent.
The American business tycoon is already the Gunners' largest individual shareholder, but has increased his power by acquiring a further slice of the club from British industrialist Ernest Harrison.
The Denver-based sports magnate is now edging towards the 29.9 per cent holding which would, under the City's financial regulations, make him obliged to launch a formal takeover bid.
Kroenke has preferred to remain quiet on his intentions for Arsenal, giving no indication as to whether he plans to assume full control at Emirates Stadium.
Any public statements regarding future bid intentions must be unambiguous, otherwise the individual or group would, under the Takeover Panel's rule 2.8, be prevented from making a formal move for six months.
Arsenal chairman Peter Hill-Wood has announced that he would have no problem with Kroenke making a bid for the club, but has admitted that he does not expect such a move to happen any time soon.