West Ham want to win the Premier League, FA Cup and League Cup this season, according to joint owner David Sullivan.
The Hammers finished 11th in the top flight after a disappointing campaign last season.
Slaven Bilic has overseen a summer of heavy spending however, signing Marko Arnautovic for a club-record fee, with Javier Hernandez arriving from Bayer Leverkusen.
Pablo Zabaleta and Joe Hart have also joined, and Sullivan is aiming high.
“I think you need a bit of luck with injuries,” Sullivan told Jim White on talkSPORT. “At the moment, Mr [Diafra] Sakho is 100% good and that would make a huge difference to the season.
“The manager is a good manager, he just needs a bit of luck. We need a bit of luck with results and refereeing decisions.
“It is very tough to get into that top seven, and Everton have spent a fortune. The top four have really spent huge money. The Man United manager [Jose Mourinho] was building us up [recently] because he wants to say ‘we are playing a tough team in our first game’.
“After Leicester, it is possible. I realise the supporters say we won’t do this and that, but we start the season in three [competitions] and the ambition is to win those three trophies.
“I know it is very, very unlikely we will do that – and any one of them would please the board – but you have to think you can win anything and on our day we can beat anybody.”