The main stadium is potentially one of the most important venues for attracting jobs and investment to the Olympic Park in east London, and a football club could affect its character, the Economic Development, Culture, Sport and Tourism committee said.
It also warned that unless action is taken on other legacy promises, "the Olympics will fail to deliver."
"The arrival of a Premier League football team in the middle of the Olympic Park may affect the character of the park and its surroundings," it said.
Football, rugby and cricket clubs have expressed an interest, the latest being the new owners of Premier League club West Ham United, but they have been put off by the organisers' commitment to retain an athletics track around the pitch.
The committee, in its last report in July, warned that without decisive action in finding an anchor tenant, the stadium "is in danger of becoming a white elephant".
Seven months on, it warned "time is running out."
The report acknowledged the Games will provide regeneration for an area of London largely neglected during the past 100 years.
It will be the largest new urban park in Europe for 150 years, and will have state-of-the-art sports buildings, new homes in the converted Olympic Village and transport improvements.
But the committee warned other legacy promises had been neglected, including jobs for locals and increased sporting participation.
It also said that if the homes envisaged only catered for the affluent moving into the area, rather than locals, the Park could become "an island of prosperity".
"More ambitious targets must be set and enforced," said the committee's chair Dee Doocey.
