Olympic and Paralympic champions have voiced their dismay at news that the stadium may not open fully until the summer of 2016.
Four bids are still being considered as full-time tenants at the Stratford venue, but each bid will require significant and time-consuming modifications.
Dennis Hone, chief executive of the London Legacy Development Committee , revealed this week that it will not re-open until August 2015 at the earliest and probably not before August 2016.
Olympic champion Jessica Ennis told Sky News it was important the stadium was opened to the public without delay.
She said: "I've some amazing memories of the stadium, like a lot of other athletes.
"I'd love to see it opened to the public as soon as possible."
Paralympic double gold medallist Hannah Cockroft said it was vital to speed up the process so that the goodwill generated by the success of London 2012 could be tapped into.
"The danger is that if it's not opened fully to the public for four years then that interest will wane," she said.
"It's an amazing venue and people want to see it, they want to be a part of it. I really hope they sort this out, they have to."
A transformation project costing nearly £300m is currently under way at the site and is expected to last up to 18 months.
The park itself will be opened to the public on July 27 next year, one year to the day the Games opened in London.
Maria Miller, Secretary of State for Culture, Media and Sport, told Sky News: "The stadium is vital for the legacy of the Games, but the important thing is to get the right tenant in."
The four bidders are West Ham United FC, Leyton Orient FC, a Formula One venture and the University College of Football Business - an academic institution owned and run by Burnley FC.
A final decision is expected in the first half of 2013, or possibly sooner.