City boss Manuel Pellegrini wants to mark his debut season in England by securing all four trophies they are in.
And Kompany, 27, says it is inevitable that City will do the quadruple at some stage in the near future.
"We can't promise it will happen now, but eventually it will have to happen," said the Belgium defender.
"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.
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"This club definitely has a target to win every competition possible."
Pellegrini's side are second in the Premier League table, lead West Ham 6-0 after the first leg of their Capital One Cup semi-final and face Barcelona in the Champions League last 16.
They progressed to the fourth round of the FA Cup on Wednesday with a 5-0 replay victory over Blackburn Rovers.
City's neighbours Manchester United secured the treble of Premier League, Champions League and FA Cup in 1998-99.
Kompany also credits Pellegrini, who replaced Roberto Mancini as manager last summer, with the greater attacking intent City have shown this season.
City have scored 99 goals this season from 33 matches and average four goals a game at home, with 64 from 16 fixtures.
"He's very offensive-minded and I think that's shown in our results and the way we play," Kompany said.
"I think we have been one of the best teams to watch in the Premier League so far."
Manchester City captain Vincent Kompany says it is only a matter of time before the club complete a record haul of four major trophies in a season.