The decision on who will take over the stadium will be made by 28 January
Olympic gold medallist Darren Campbell says plans for the 2012 athletics legacy to exist away from the Olympic Stadium should be considered.
Tottenham Hotspur want to demolish the 2012 venue and re-build it without a running track, instead redeveloping the Crystal Palace athletics stadium.
The Spurs plan proposal been widely opposed by the athletics community.
But sprinter Campbell said the Olympic Stadium could become a "white elephant" if the right decision is not made.
West Ham's rival proposal
would see them move to the Olympic Stadium from Upton Park and keep the athletics track for elite events and community use in a 60,000-seat venue.
Critics of the Hammers' plan have queried whether the track would dilute the atmosphere, with some also suggesting the view of the pitch from thousands of seats would be poor.
Campbell, who won relay gold at the
2004 Athens Olympics,
told BBC Manchester: "If it's not going to be sustainable to have a track [at the Olympic Stadium] and it becomes wasted, then we haven't created any form of legacy.
The National Sports Centre has seen better days
"One compromise being talked about is a refurbishment of Crystal Palace. For me, I think, if it was a case that they knocked down Crystal Palace, and re-built it I would have no problem.
"I would much prefer to see a stadium being used than not. If we look at what happened at the City of Manchester Stadium, then that's an example of how it can work."
Tottenham's proposal has also been supported by the chief executive of Bromley Borough Council, which owns Crystal Palace Park, within which the athletics stadium - part of the National Sports Centre (NSC) - is located.
Doug Patterson said: "The Spurs plans would be positive for the area because I am not sure what else would happen. There are not any other significant plans. Nobody has got the money to spruce up Crystal Palace.
"South Londoners would benefit with the Spurs plans. They would not have any direct benefit from the West Ham plans."
Patterson claimed that Tottenham's redevelopment of the site as a 25,000-seat venue would return it to its "previous standards".
Crystal Palace is a world-famous athletics venue but the complex, which opened in 1964, is badly in need of a multi-million pound refurbishment.
The lease for the National Sports Centre is held by the London Development Agency, but Bromley would be the planning authority who would need to approve any plans to substantially change the site.
Another complicating factor could be a proposal by Crystal Palace Football Club to relocate from Selhurst Park to a redeveloped NSC. The club are set to outline their plans on Thursday.