The former Labour leader is also expected to reveal how the controversy around the controversial resignation of garda commissioner Martin Callinan almost resulted in the junior coalition partner walking out of government.
Mr Gilmore describes how Ms Burton was disappointed at not being given the position she wanted in 2011, when she was appointed social protection minister.
He is expected to outline how his relationship with Ms Burton was fraught and tense.
When Ms Burton then took over as leader last year, he describes how he was taken out of government and essentially “court martialled” and “shot at dawn”.
The memoir, entitled Inside the Room: The untold story of Ireland’s crisis government, outlines his period in the tánaiste’s office from 2011 until 2014 and is being published by Merrion Press.
The book is also expected to outline how Labour were close to leaving government after the controversial resignation of garda commissioner Martin Callinan. Taoiseach Enda Kenny had sent a civil servant to the garda chief’s home saying the government were unhappy after it emerged calls had been recorded in Garda stations for years.