The LLDC said it was assessing proposals from the two, as well as from Leyton Orient Football Club and the UCFB College of Football Business, without saying when a decision was due.
Formula One supremo Bernie Ecclestone told Reuters he was not directly involved in the motor-racing bid which LLDC said was made in association with a company called Intelligent Transport Services.
"If they were to get permission to do it [use the stadium for a Grand Prix], then we would be more than happy to do something with them. But we have nothing to do with putting in a bid," he said.
"London is further ahead in planning legacy than any previous host Olympic city," LLDC chairman Daniel Moylan said.
Some local politicians fear the 80,000-seat venue could become a white elephant. A previous plan to sell the stadium to West Ham fell apart in October with the government citing "legal paralysis" after Premier League club Tottenham Hotspur, which had a bid turned down, challenged the decision.
