The Gunners’ season ended in humiliation, missing out on a top-four place and surrendering the Europa League final 4-1 to Chelsea.
Boss Unai Emery’s transfer funds have taken a hit as a result, with the Spaniard only set to be granted around £40m to spend this summer.
He could boost that figure by selling players first, and Morgan reckons four or five could be shown the door.
Ozil arrived from Real Madrid in 2013 and was hailed by Arsenal fans as the playmaker who would take them to the next level.
“But now Ozil is earning £350,000 a week to sit there like a lazy warthog and it’s time we shipped him out.”
Morgan was speaking ahead of this year’s Soccer Aid at Stamford Bridge on Sunday, where the Good Morning Britain presenter will co-manage the World XI alongside Harry Redknapp.
And he took great delight in mocking rivals Manchester United and Chelsea when suggesting he has the experience ready to manage them.
Morgan added: “I’ve waited a long time for this. It’s time for my managerial skills to do the talking. I’ve done a lot of talking about managers over the years.
But the club has gone backwards in recent seasons and now face a third consecutive year in the Europa League.
Morgan laid into the former German international, and says he should be the first to be shipped out by Emery.
“He’s [Emery] got a massive job to do. I would kick out four or five of those wastrels,” he said.
“That performance at the end of the season was diabolical and he can start with Mesut Ozil, who I’ve defended on talkSPORT before.
“I’ve done one of these games before, a charity game at Leicester, against Niall Horan’s team and I won that, so my record as a manager is one for one, which I think makes me the best manager in the world right now.
“If I was to win on Sunday as well it becomes two for two and that’s the sort of stuff when you start getting calls from Chelsea and Man United.”
Morgan may be disappointed to learn that his chances of replacing outgoing Chelsea boss Maurizio Sarri have taken a hit.
The Italian is set to be replaced by Blues legend Frank Lampard, who led Derby to the Championship play-off final last season.