City put one foot in the Capital One Cup final last week when they thrashed West Ham 6-0 in the first leg of their semi-final, while they also qualified for the FA Cup fourth round with a 5-0 win over Blackburn Rovers on Wednesday, sit second in the Premier League and remain in contention in the Champions League.
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Manuel Pellegrini says City can become the first English club to win those four competitions this season and, while Kompany would not set a timeline, the Belgian defender remains confident they can do it one day.
"We can't promise it will happen now, but eventually it will have to happen," the Belgian told reporters.
"We are the players at the moment who have been chosen to do it. If it's not us then it will be other players.
"This club definitely has a target to win every competition possible."
City's attacking prowess has been critical to their success so far during the 2013-14 season with Pellegrini's side scoring their 99th goal in all competitions in the win over Blackburn.
And Kompany has hailed Pellegrini's attacking focus in his first season at City since the Chilean manager replaced Roberto Mancini at the Etihad.
"He's very offensive-minded and I think that's shown in our results and the way we play," Kompany added.
"I think we have been one of the best teams to watch in the Premier League so far."