The marketing publication Campaign Life reports that Thompson wanted to start with a clean slate and picked replacement agency Lucky Generals without a formal pitch.
Lucky Generals has been lined up to become the bookmaker’s agency of record.
Thompson recently replaced Christian Woolfenden, who was promoted at the end of 2014.
BMB was picked to handle Paddy Power’s £20 million advertising account after a four-month competitive pitch, run by Oystercatchers, that was completed in March this year.
Although Lucky Generals had an existing relationship with Paddy Power, the agency did not put itself forward for that pitch.
Lucky Generals was recently appointed as Twitter’s first retained advertising agency in the UK.
Juliet Haygarth, BMB’s chief executive, told Campaign: “The new marketing director arrived at Paddy Power on Monday and, by the end of the week, he had moved the account to Lucky Generals.”