Kroenke has come under severe criticism from Arsenal fans ever since his arrival at the club 10 years ago.
The 70-year-old rarely attends matches and was absent from the Carabao Cup final loss to Manchester City yesterday.
Wright claims Kroenke seemd to make it clear he does not care about Arsenal by awarding Arsene Wenger a new two-year contract last summer despite a large section of support being against the Frenchman.
Gunners legend Wright has demanded Kroenke has a more hands-on role at the club.
“Kroenke doesn’t care enough, Kroenke doesn’t care,” Wright said on BBC Radio 5 Live.
“If he cared then Arsene Wenger would not have got a two-year deal with everything that’s happened.
“With what’s happening now, why is it that everybody else, all the fans, everyone who loves Arsene Wenger, are starting to see now that it’s getting to a point now where we feel he should go? With the banners, with the Wenger out.
“The owner should come in, sit down and be here and say ‘what’s happening? How’s this working? What are we going to do about this? How are we going to get ourselves back to where the fans want us?’.
“At the end of the day no one is paying any attention to the fans, they’ve been saying it for years what they want, no one is taking any notice.
“The fact is the owner has not done anything like that and he’s just literally given Arsene Wenger carte blanche to keep on doing what he’s doing.
“Arsene Wenger keeps doing what he’s doing, there’s no accountability for the players, there’s no consequence to their poor performances, there’s no consequence to their inconsistency and so they will continue doing what they are doing.”