The former deputy prime minister makes the revelation in a memoir of his time in power in which he says David Cameron did not seem to be surprised that he wanted to stop personally dealing with Mr Gove, adding that Number 10 "clearly loathed Gove's principal adviser at the time".
Mr Clegg said Mr Gove was "charm personified" when they had dinner together in Putney soon after the coalition was formed, according to The Guardian which is serialising the memoir.
An extract from the book in the newspaper states: "A little over three years (after the Putney dinner) our relationship had soured to the point that he banned Lib Dem special advisers from physically entering the Department for Education, hid on one occasion in the toilet to avoid speaking to David Laws, and let loose his somewhat unhinged advisers to brief against me, and even against Miriam, in the press."
The extract goes on: "On one of the last occasions I spoke to him in government, I asked him to come and see me in my office. He was keen to be accompanied by his assistant, but I insisted we meet alone, as I wanted to deliver a blunt message.
"Once we were alone, I asked him how he would react if someone on my behalf wilfully lied about his wife in the newspapers? (Miriam had, ludicrously, been accused in The Mail On Sunday by one of Michael Gove's advisers of seeking a Whitehall contract for a children's book charity - the contract had in fact been decided by Number 10). He mumbled that he thought he 'knew what had happened'. I was livid."
According to The Guardian, Mr Clegg says he told Mr Cameron soon afterwards that he was not prepared to "waste (his) time working with Michael Gove" and that Mr Laws would do so on his behalf.
"Given how much No 10 clearly loathed Gove's principal adviser at the time and were as exasperated as I was by his occasional public outbursts, this didn't seem to come as much of a surprise to Cameron," Mr Clegg writes.
Mr Clegg's book is called Politics: Between The Extremes.
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