The Hammers suffered a disappointing campaign last term, finishing 11th in the league while suffering early exits in both the FA Cup and the Europa League.
"I think you need a bit of luck with injuries. 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," he told talkSPORT.
"The top four have really spent huge money. The Manchester 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 [won the league in 2015-16], 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. Leicester was something we all thought could not happen, but they showed it can happen. I'd settle to win a cup...and I'd love to go to Wembley and win a cup.
"Last year [in the EFL Cup] we beat Chelsea at home then got Man United away in the next round, I mean you are not going to win anything with draws like that. Then we get Man City in the third round of the FA Cup, Arsenal get non-league teams. We have been very unlucky with the draws - we get away draws - Arsenal get more home draws than any other team I've seen. We are due an easy, easy cup draw."
West Ham begin the new league season away to Manchester United on August 13.