The Citizens face Blackburn Rovers at Etihad Stadium on Wednesday night in their FA Cup third-round replay as the home side look to set up a clash against Watford.
We must have the mentality to try to do it [quadruple]
City are going strong on all fronts this term, having virtually sealed their spot in the Capital One Cup final courtesy of a 6-0 first-leg win against West Ham United.
And Pellegrini wants City to approach the crucial final months of the season with the mentality that they can win all four trophies this term.
“We know that during the season, with injuries and the amount of games you have to play, it is very difficult,” Pellegrini told BBC Sport.
“That’s why nobody has done it before. But I think we must have the mentality to try to do it.
“But we’re not thinking of winning the four competitions, we are just thinking of winning the FA Cup tie against Blackburn.”