Director of football Sven-Goran Eriksson was charged with finding the new boss and the Swede opted to turn to his countryman and former assistant at Manchester City and the Mexico national team Hans Backe, who signed a three-year contract on Tuesday.
"Roberto Mancini was up there in our thinking, Sven and I met with him and he is a fantastic man," said Trembling in the Nottingham Evening Post.
"He is without doubt a fantastic coach, he could come into the club and do something from a PR point of view and he would put bums on seats. But I did not want a particularly high-profile appointment because we have had a media circus around the club for the last three months.
"It was important that we got somebody who would get on with the job and concentrate on the football side of things. I am sure Roberto would have wanted to do that, but I don't think the media circus would have allowed it."