Ms Burley, who has more minutes on live TV than any other presenter, said Mr Cleverly was meant to be in the seat but had not turned up.
Mr Cleverly, who faced grillings elsewhere this morning on a “doctored” clip shared by the Tories and Jacob Rees-Mogg’s Grenfell comments, said he was being interviewed by talkRADIO when Ms Burley began her rant.
Ms Burley said: “I’ve got an empty chair here. It was supposed to be filled by the chairman of the Conservative Party.
“He is probably 15 feet away… just at the moment. I’ve been in to see him during the break, he said he wasn’t due to come and talk to us today, although they had said that they would talk to us.”
She went on to raise points she had hoped to address with him, including Boris Johnson likening Jeremy Corbyn to Stalin, the Grenfell comments row, the row around Alun Cairns, the Brexit transition period and the Russian interference report.
Ms Burley pointed to the chair and said “there you go, there’s your empty chair”.
“I know that Number 10 Downing Street watch our show,” she said. “I know that the spin doctors at Number 10 Downing Street had absolutely reassured me via text that when politicians were doing the rounds in the morning they would be doing this programme.
“Yet we have an empty chair.”
Mr Cleverly has since shared details of a talkRADIO interview with Julia Hartley-Brewer he did this morning and tweeted: “This is the radio interview I was booked in to do, and was doing, when Sky News cut to an empty chair.”
He added: “I’m good at multitasking but cannot be in two studios at the same time.”
It comes after Mr Cleverly had a spat with Piers Morgan, over a video of Sir Keir Starmer that the Tories edited.