The former Gunners star wants the club's majority shareholder - often dubbed 'Silent Stan' - to "start answering some questions" about a rumoured sale to a Middle East consortium
The club recently moved to deny any contact had been made between the American businessman and potential buyers over a possible £1.5 billion bid, stating the 65-year-old is committed to the club "for the long term."
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"He is known as 'Silent Stan', but it's time Stan Kroenke started speaking," he wrote in The Sun. "Arsenal's majority shareholder needs to start answering some questions and tell everyone what his detailed plans are for the club.
"I want Kroenke to start engaging with the fans. Looking at all his sports teams, I'm not sure any of them actually win anything. Now the Gunners, unfortunately, will be going an eighth year without winning a trophy.
"He rarely goes to games, so you have to wonder whether he cares about the club. He seems more interested in having a business, which makes a lot of money. That's why I don't think he will sell his shares to anyone."
The Gunners are in danger of missing out on Champions League football for the first time under Arsene Wenger after losing to rivals Tottenham 2-1 on Sunday and Wright wants to know why Kroenke is not prepared to spend big to bring top players in to the side.
"I am not in the greatest of moods after seeing Arsenal lose to Spurs," he continued. "Many Arsenal fans will feel exactly the same as me. It's all about bragging rights. Yet at the moment, the neighbours are moving ahead.
"I understand why [Ivan] Gazidis and Wenger do not want the club turned into a Chelsea-style outfit which spends colossal sums on players.
"But the club needs to offer the going rate in wages to players like Juan Mata who, it appears, was ready to join Wenger. Kroenke must explain why he is not prepared to go the extra mile for these excellent players."