The Championship club whose current 35,000-seat Upton Park stadium is near the Olympic Park in East London said on their website that they were in the running.
The Olympic Park Legacy Company (OPLC) confirmed four bids had been received.
"The Legacy Company will shortly start its evaluation process with the aim of announcing which concessionaires will occupy the stadium alongside athletics," an OPLC spokesperson said.
"Legacy planning is further ahead than any previous Olympic host city. The stadium will become the new national centre for athletics and host of the 2017 world athletics championships and we remain on course to reopen the stadium as a multi-purpose venue in 2014."
West Ham's vice-chair Karren Brady said the club, third in the Championship and hoping for an immediate return to the Premier League after relegation last season, had bid with the backing of UK Athletics.
"We have not taken this decision lightly and I should be clear that any move to the stadium is conditional on the fact that it must provide an arena that is fit for world-class football and feels like home to our deserving fans," added Brady.
The 500 million-pound stadium has already been named as venue for the 2017 World Championships but an initial deal for West Ham to take over the facility collapsed last October following a legal challenge.
Bids were invited in a new process that ended on Friday, with a decision expected in two months' time and before the Games open on July 27.
Conversion of the stadium to a 60,000 seat ground from the 80,000 Olympic venue should be completed by 2014.
West Ham's co-chairmen David Sullivan and David Gold said in a joint statement that they were fully committed "to making it our home for at least the next 99 years."
