The Sheffield stadium where Jessica Ennis trains could be demolished in a bid to save money, according to a document seen by the BBC.
The document shows Sheffield City Council could save £500,000 per year if the Don Valley Stadium was to close.
The council said no decisions had been made and this was just one of a list of money-saving options.
Ennis's coach, Toni Minichiello, said the Olympian would remain in the city even if she had to train elsewhere.
The document, seen by BBC Radio Sheffield, raises the possibility of reopening the city's smaller Woodburn Road Athletics Stadium which was closed 18 months ago to save money.
Mr Minichiello said the stadium was crucial for the gold medallist's outdoor training.
"If we don't have an outdoor track to work on then we'll have to find some options in other places but she'll stay in Sheffield because that's where she wants to be.
"It's very sad that it's got to this point."
Don Valley stadium opened in 1991 for the World Student Games in Sheffield at a cost of £29m.
The full cost of the Games was revealed in 2011 as £658m.
The Student Games debt is not due to be paid-off until 2024.
Sheffield Eagles rugby league club still play some games at the Don Valley Stadium, but Rotherham United's short tenancy there ended after the club moved in to its own stadium in July last year.
Mike Corden, chairman of City of Sheffield Athletics Club, whose members train at Don Valley Stadium, said its closure would be an "obvious blow" to the city's athletes.
"I would be fighting tooth and nail to make sure we keep a top-class facility open so we can develop the Jess Ennises of the future," he said.
"I would hope the council, if they do ultimately close this place down, will offer us a first class alternative."
Sheffield City Council said the document seen by the BBC showed a number of options drawn up by council officers for consideration as councillors decided the authority's budget for the coming year.
Bryan Lodge, cabinet member for finance at Sheffield City Council, said the council faced "tough options".
It faces making £50m of cuts in 2013-14 on top of £140m cuts already made in the last two years, said Mr Lodge.
"We're making decisions on a lot of things which are very difficult and very unpalatable to a lot of people."
Sheffield councillors have until 4 March to finalise the city's budget for the coming financial year.