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."

Zac Mitchell, 20, was injured in April while working on a remote farming property in Western Australia.
"A bull kicked my hand into the fence," Mr Mitchell said of the incident.
He underwent two unsuccessful operations to reattach his thumb before doctors opted to relocate his big toe in surgery lasting eight hours.
Mr Mitchell said fellow workers had attempted to preserve his thumb immediately after the accident.
"They put it in the esky [cooler] with some ice," he told the BBC.
Mr Mitchell was flown to hospital in the state capital of Perth, but efforts to save his thumb ultimately failed.
Despite initial reluctance, the cattle worker agreed to the transplant operation at the Sydney Eye Hospital two weeks ago.
Lead plastic surgeon Dr Sean Nicklin said he was not surprised it took time to accept.
"It is a bit of a crazy idea - they [patients] do not want to be injured in another part of their body," he said.
"[However] even if you have got four good fingers, if you do not have something to pinch against them, your hand has lost a huge amount of its function."
Mr Mitchell will need more than 12 months of rehabilitation, but he plans to return to farm work.
The Sydney Eye Hospital said it was rare to transplant a complete toe, like in Mr Mitchell's case, although partial toe relocations were more common.
"A lot of people think their balance and walking is going to be significantly affected which it generally isn't," Dr Nicklin said.
Mr Mitchell's mum, Karen, said he was making a good recovery.
"Two weeks since the operation his walking is almost back to normal."
Doctors say Mr Mitchell should eventually be able to return to his hobby of bull riding.
Reporting by the BBC's Greg Dunlop
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.
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An Australian cattle worker whose thumb was severed by a bull has had his toe surgically transplanted in its position.