A host of top coaches have been linked with the vacant post at Meadow Lane, with the ambitious League Two outfit keen to make an appointment as soon as possible.
Director of football Sven-Goran Eriksson has been leading the search for Ian McParland's replacement and is reported to be closing in on his preferred candidate.
However, Trembling claims a selection will not be made based purely on the profile of the manager in question.
"It is not just about the name. The next manager has to tick all of the boxes and fit in with what we are doing," Trembling told the Nottingham Evening Post in the wake of reports linking the likes of Neil Warnock and Roberto Mancini with the club.
"Sven is a genius. He knows what makes a good manager.
"We are privileged to have him in charge of the football side and he will work closely with whoever he brings in."
Trembling has pointed out that County are in no rush to get a new manager in place, but he has hinted that the appointment process is edging towards a conclusion.
"We have to take our time and go through everything in detail," he added.
"We know we can do that because the professionalism of the staff and the players gives us stability.
"They have been a credit to themselves and the club.
"Sven has got two favourites and it has to be the right appointment for the short-term and the long-term."