The followers of the North West club are keen to display their backing of the Italian even if his side fail to clinch the Premier League title this season.
Reports have also claimed that the 47-year-old could be axed by the club's Abu Dhabi owners in the summer, but supporter Andy Savage, who runs the mcfcforum website, has stated that the fans will not blame the club's heirarchy if Mancini does depart the Etihad Stadium.
"There has been a lot of pressure on the manager from the London-based press," Savage told the Manchester Evening News. "We decided to show that, even if we finish second, we are sick of chopping and changing.
"If Mancini goes at the end of the season, it is not in any way, shape or form a criticism of the owners or the board. But if he does go we want to respect the work he has done so far.
"We would prefer to see him see out the remaining year of his contract, or even better get a new one. There are also rumours that Roberto may want to go back to Italy, as his father has been in poor health - we just want to show our support whatever happens."
Almost 1,000 fans have signed the online petition for the Respect Mancini campaign, which was launched last week.