The Guardian Unlimited website reports that the stadium, which will be the centrepiece of the Olympic Park in east London if the city is successful in its bid, had been expected to pass to a football club after the games, with West Ham the most likely tenant.
However, instead of being leased in the way the Commonwealth Stadium in Manchester passed to Manchester City, the intention is to reduce the stadium's capacity and use it to attract other international events to the capital, Livingstone said.
There is a possibility that the stadium could be used by a rugby club but football has been ruled out as a partner because of the more onerous fixture list.
"Sadly West Ham will not get the stadium," Livingstone told a London 2012 fringe meeting. "Instead we will scale the stadium down to around 25,000 or 30,000 seats and treat it as an athletics facility."
He said the decision not to pass the stadium on was a "more creative" option and that a lasting athletics legacy in the capital would be a more attractive option for International Olympic Committee members when they came to examine London's bid.
