Essex have held talks with the London Legacy Development Corporation (LLDC) about playing at the venue, which will have West Ham as the anchor tenant from 2016.
Essex chief executive Derek Bowden told BBC Essex: "I had a conversation with the LLDC a few weeks ago and they're very keen for there to be a cricket festival. Not before 2016 because there is work to be done. But we're keen to do it."
He added: "The conversations I've had have been about a two-week window where we, and maybe a few other counties, play cricket there to maximise the use of the stadium and mitigate the investment needed to convert it for cricket."
The Olympic Stadium will also be a venue for the 2015 Rugby World Cup and will host the 2017 World Athletics Championships.
- Sports & Recreation