The London Legacy Development Corporation board is meeting on December 5 and sources close to the process say it is expected that the football club will be given a major step towards becoming the stadium's tenants.
Preferred bidder status will not involve the signing of any contracts but will put West Ham in the driving seat to securing a new home under a 99-year lease.
The funding gap for converting the stadium into a football ground with retractable seating over the running track is understood to now be down to around £20 million after West Ham and Newham Council agreed to put in more money.
There is now set to be further efforts to secure the final outstanding cash with approaches to the Treasury and the London mayor's office.
Even so, the total cost will be at least £160m and one lingering fear is that those costs could spiral in the future, with a key element of future negotiations being who would underwrite any such increases.
The Hammers are one of four bidders hoping to be chosen as the new anchor tenant for the Olympic Stadium, which has cost £486m so far and has been vacant since hosting the closing ceremony to the Paralympics at the start of September.
The Premier League club are competing against League One side Leyton Orient, a football business college and a group keen to bring Formula One racing to the Olympic Park.
West Ham's latest offer is believed to be a £15m upfront contribution, a £5m improvement on the original offer, as well as rent of £2.5m a year and £6m-a-year income for the LLDC from stadium naming rights and catering revenues.
The LLDC confirmed this month that the stadium will not re-open until 2015 at the earliest and possibly the summer of 2016 - which would be two years later than expected.
- Sports & Recreation
- West Ham