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.
The process to select a main tenant for the stadium in East London was extended by eight weeks in May after the LLDC said some 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 in a statement.
There has been speculation that Formula One plans 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 last October with the Government citing "legal paralysis" after Premier League club Tottenham Hotspur, who had a bid turned down, challenged the decision.
The LLDC also said a bid to turn the one 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 and criticised the selection process.
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.