A number of online campaigns have been launched calling for the broadcaster and Good Morning Britain host to take up the highest political position of power.
On Monday, Secretary of State for Work and Pensions Thérèse Coffey turned off her video call camera following a difficult interview with Morgan.
And earlier this month, Health Minister Matt Hancock’s awkward interview about how he did not vote for free school meals was shared widely online.
Morgan also grilled Education Secretary Gavin Williamson during a heated exchange last week and asked the minister: "What will it take for you to resign?'
Speaking on the show on Tuesday, Morgan admitted he quite liked the idea of the political top job.
“It has got a ring to it, and could I do any worse is the real question,” he said. “That’s the real calculation for the British people as they wake up this morning to this huge campaign. Could I do any worse?”
Morgan co-hosts the morning news show with Susanna Reid.
It comes just days after Morgan, the former editor of The Daily Mirror, admitted he plays up to his tough persona while working.
He said that instead of chasing confirmation from colleagues and guests, he aimed to be “divisive and polarising” in the hope of waking people up in the mornings.
Appearing on Gabby Logan’s The Mid.Point Podcast, where he is the first guest of series two, Morgan spoke about his public image.
He said: “Look, there’s a persona that I certainly play up to. I think all television is performance in a way. I certainly think there’s a sort of theatrical element to it as well.
“I certainly play up to that, I don’t chase around trying to be beloved, it would be a fairly lonely journey if I did. So, I prefer to be divisive and polarising, and get everybody going and wake everybody up in the morning.
“It’s the title of my book, you know, Wake Up, however when I do get home and shut the door I’m like everybody else, and I get a nice bottle of wine out, have a chat with the kids, talk to my mum and dad, watch a bit of telly. I’m a sea of serenity.”