Morgan is one of Wenger’s harshest critics and yesterday’s Carabao Cup final loss to Manchester City has only strengthened his views.
Arsenal were beaten 3-0 by Pep Guardiola’s side but it was the performance, more than the scoreline, that upset fans.
Several thousand Arsenal fans left before the final whistle yesterday and Morgan says that is a telling sign they have had enough with Wenger.
When asked if Arsenal fans should boycott the club, Morgan told talkSPORT: “Yes.
“I think you have to do something dramatic because at the moment the board is able to hide behind the fact that, whenever Arsenal fans do protest, it’s never that big a protest.
“I think the real issue for Wenger yesterday was the sheer volume of Arsenal fans who left before the end.
“I never leave before the end – I will stick it out even if we are getting hammered, if I believe the team are putting in even half an effort.
“Yesterday, I left 15 minutes before the end!”
To the frustration of many fans, Arsene Wenger signed a two-year extension at Arsenal last summer.
The Gunners have once again struggled this season and are relying on winning the Europa League in order to qualify for next term’s Champions League.
Piers Morgan says it is down to the board to sack Wenger because the Frenchman will never give up the money he is earning.
“So we are sixth in the league, we are 27 points off the top – we are 11 points behind Tottenham for Christ’s sake! That’s how bad things are!,” he added.
“We’ve been dumped out of the League Cup final in humiliating fashion, we got dumped out the FA Cup by Nottingham Forest, we are about to get hammered, I would imagine, by AC Milan in the Europa League that none of us want to be in anyway.
“So we won’t qualify for the Champions League for the second year running.
“I’m just not sure what more Wenger has to do before the normal yardstick for failure is applied to him, and he is sacked.
“I’m way beyond the stage of expecting Wenger to quit – he’s not going to quit.
“He earns tens of millions of pounds a year to manage failure!”