West Ham co-owner David Sullivan believes his team can win the Premier League title after an impressive start to the 2015-16 season.
The Hammers are third in the top flight after collecting 20 points from their opening 10 games, trailing table-toppers Manchester City by two points.
New Upton Park boss Slaven Bilic has led his side to wins at title hopefuls Arsenal, City and Liverpool as well as beating champions Chelsea 2-1 last Sunday, and Sullivan has high hopes for the East London club ahead of Saturday's visit to Watford.
"We're very, very optimistic," the co-owner told the Hammers' official website. "I'm not talking it down I want to talk it up -- I believe it's achievable.
"It's a big myth, I mean look at what's gone wrong with Chelsea -- that looked an impossibility -- so why shouldn't the opposite happen to us? In football, we're here to dream."
The Hammers were knocked out of the Europa League and Capital One Cup early on this season, but Sullivan says Champions League qualification is a realistic aim before the club move to the Olympic Stadium next season.
"At the start of the season we were in four competitions and the aim was to win those four," he said. "Now we're down to two -- we've got the big double left -- and it's very, very unlikely but not impossible.
"If you'd asked about the Champions League at the start of the season I would have said it's impossible this year -- but it's not. Forget dreaming in the future.
"The unfortunate thing is that if you finish fourth you have to play a qualifying game -- and no doubt we'd get a real toughie -- like the fourth best team in Spain or Italy.
"Realistically, I'd love fourth place and we'd take our chances. I know it's unlikely, but it really is possible.
"One more win and we could be top of the table, looking down. I'm not sure how clever that would be as it'd really put pressure on people but it's not bad to be two points off the lead."
Hammers striker Mauro Zarate told ESPN FC on Tuesday that his team must remain "realistic" about their chances of winning the Premier League title, but believes finishing in the top four is a possibility.