Former Inter Milan coach Mancini was the most high profile name linked with succeeding Ian McParland at Meadow Lane after the Scot was sacked just over a fortnight ago.
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.
However, Backe has indicated this contract could be his last job in club management, and Trembling refused to rule out the possibility of considering Mancini again in the future when the club are closer towards their five-year goal of bringing Premier League football to Meadow Lane.
He added: "Well, maybe in the future. Hans is on a three-year contract and who knows what Roberto will do now? He has said publicly he is looking to get back into a coaching role.
"So who knows what he will be doing in three years time? If he is available in three years time and we are looking for a manager at that point, who knows?"