The cabinet minister was interrogated on when the prime minister would face the veteran political broadcaster during an interview on BBC Radio 5 Live.
Mr Gove was asked ”On a scale of one to 10, what’s the chance of the Andrew Neil interview with Boris Johnson happening? Just give us a number.”
He replied: “Erm, I think the number would be 0207 930 4433. That’s the Downing Street number. And if you ring the prime minister’s diary secretary, he will know, or she will know, what the prime minister is going to do. I’m not the prime minister’s diary secretary.”
When The Independent called the No 10 switchboard, a recorded message played, saying: “Hello, you have reached the Downing Street switchboard. We are unable to give out any information relating to the prime minister’s diary.”
A spokesperson for Downing Street said they did not know if the switchboard had received more calls than usual after Mr Gove gave out the number, but said they had been able to get through to the switchboard as normal.
It comes after Mr Neil concluded his general election interview with Nigel Farage by taking several minutes to criticise Mr Johnson for not arranging an interview.
He told viewers he had planned to hold the prime minister to account on issues of trust, but said the Tory leader had not agreed to an interview despite weeks of negotiations by the BBC.
“Leaders’ interviews have been a key part of the BBC’s prime-time election coverage for decades. We do them on your behalf to scrutinise and hold to account those who would govern us. That is democracy,” Mr Neil said.
On Thursday night, Mr Neil said he had an “oven-ready” interview for Mr Johnson.
“The theme running through our questions is trust,” the presenter said. “And why, so many times in his career in politics and journalism, critics and sometimes even those close to him have deemed him to be untrustworthy.
“It is, of course, relevant to what he is promising us all now.”
He outlined policy issues on which he would question Mr Johnson, saying: ”He vows that the NHS will not be on the table with any trade talks with America. But he vowed to the DUP, his unionist allies in Northern Ireland, that there would never be a border down the Irish Sea.
“That is as important to the DUP as the NHS is to the rest of us. It is a vow his Brexit deal would seem to break.”
He concluded: “There is no law, no Supreme Court ruling, that can force Mr Johnson to participate in a BBC leader’s interview.
“But the prime minister of our nation will, at times, have to stand up to President Trump, President Putin, President Xi of China. So we’re surely not expecting too much if he spent half an hour standing up to me.”
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