The Hammers joint-chairman is in confident mood ten games into the season.
The Hammers have made a fantastic start to the campaign and currently occupy third position – just two points off first place Manchester City.
Sullivan was keen to point out that although West Ham winning the league may seem like the stuff of fantasy, stranger things have happened in football.
“We’re very, very optimistic. I’m not talking it down I want to talk it up, I believe it’s achievable,” said Sullivan on whufc.com.
“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. At the start of the season we were in four competitions and the aim was to win those four.
“Now we’re down to two – we’ve got the big double left – and it’s very, very unlikely but not impossible,” he added.
Sullivan’s words may seem slightly outlandish but given the way the Premier League has gone this season, his optimism is understandable.
A failure on the part of the so-called bigger teams in the division to truly stamp their mark on the league, coupled with West Ham’s excellent performances, have sent expectation levels through the roof at Upton Park.
Their triumphs over Arsenal, Liverpool, Manchester City and Chelsea have proven their ability to compete directly with the big boys, and if they can add consistency in their less glamourous fixtures – a truly special season could unfold.