The health secretary said he felt like viral sensation Brenda from Bristol when thinking about the prospect of another general election.
A clip of Brenda went viral in 2017, when she expressed her horror at voting again, telling a reporter: "You're joking?! Not another one? For God's sake I can't honestly - I can't stand this."
Appearing on the breakfast show, Mr Hancock joked he felt the same.
"No! A general election, honestly? I feel like Brenda in Bristol," he told talkRADIO's Julia Hartley-Brewer.
"That is not a good idea. A general election would involve delaying Brexit further."
Turning his attention to the Brexit impasse, the politician said the only way to break the "deadlock" was by voting through the Prime Minister's deal.
"Parliament is quite clear it is willing to legislate in order to stop a no-deal, so the best way through it is to vote for the Prime Minister's deal.
"It is the best option available to deliver on the result of the referendum."