Former City and Leeds defender Danny Mills has even said a successor could be appointed by Thursday if Mancini's last realistic hope of winning silverware is ended.
Mancini, speaking at a press conference to preview the fifth-round tie, said: "We started our project three years ago.
"In three years we are always on the top - we fight for the title, we have won three trophies, we have the chance to win more this year.
"All the people who talk about this don't understand football.
"Because if Manchester City should sack me, the other 20 teams in the Premier League should be without a manager."