Warren - a lifelong, passionate Gunners supporter - pulled no punches as he accused the north Londoners of having a "losers' mentality" and Wenger of "not buying in the right players".
He told the Daily Star Sunday: "I think it is time for a change of manager and a change upstairs as well.
"I know some Arsenal fans I speak to are totally fed up with it all and maybe it needs a new broom in there.
"Off the field, they are doing fantastically as far as finances are concerned but on the field they are not doing the business.
"I think that is for various reasons. The decline of the Arsenal football team coincides with the decline of the France national side. We had the best of the France team playing for us.
"But Arsene's policy of bringing youth through and building teams around the likes of Cesc Fabregas and so forth has now gone.
"He's now having to buy in players but he has not bought in as well as some other managers have - and I don't think the club is spending the sort of money they should.
"It's all very well making these profits but us fans want the bar raised from the mentality of just qualifying for the Champions League.
"We should be saying 'we can win the Premier League'."