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.
The process to select a main tenant for the stadium in east London was extended eight weeks in May after the LLDC said parties had been discouraged from bidding because of unresolved issues including stadium-naming rights.
"London is further ahead in planning legacy than any previous host Olympic city," LLDC chairman Daniel Moylan said.
There has been speculation that Formula One planned to use the stadium and neighbouring land to create a motor-racing circuit.
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.
The LLDC also said a bid to turn the 1 million square foot Olympic media centre into offices, research labs and a data centre was now the preferred choice.
A plan by the so-called iCity consortium is the favourite after the only other bidder withdrew last week.
The consortium is backed by data centre manager Infinity and property company Delancey. It plans to create more than 4,000 jobs.
The LLDC said it will name the residential developer selected to build the first neighbourhood of housing on the park next week.
