An Olympic indoor sports arena could be heading to the city after the London 2012 games.
Leicester City Council is hoping to snap up one of the stadiums, which are being specially built for the event.
After the games, venues will be taken apart and relocated around the country. Bids are being invited for them.
The city council has already submitted an expression of interest to Sport England for one of the arenas.
City councillor Rory Palmer said: "A 5,000-seat indoor arena is the one thing that many people recognise is missing from our range of facilities.
"We would want it to be as versatile as possible to be able to host many different types of events, international sports events, community events and entertainment as well."
He said a lot of work still had to be done to look at exactly what was needed in the city and how running costs would be met.
Camapigner Tony Robinson, of Leicester, has been organising a petition for an arena in the city. He said: "While 5,000 seats would be a little short of what is really needed for Leicester, it would still be a dramatic improvement.
"What is even more encouraging is that the city council is giving the provision of such a facility serious thought.
"This can only give hope to everyone who wants to see an arena in Leicester.
"If this is the only option, then at least Leicester would get a much-needed building.
"If the bid is not successful, an arena is still needed and hopefully with a bigger capacity."
Council bosses do not know where the building would be located, other than to say they will be considering a number of empty spaces across the city.
The proposal is included in the city's strategy for the 2012 Olympic Games, which was launched yesterday.
The strategy includes the hope that Leicester can produce a gold medallist in 2012.
Other plans include establishing a number of training camps for international Olympic and Paralympic teams.
There are proposals to build a water-based artificial-turf pitch to attract athletes.
In the city centre, there could be a big screen to show sporting events to large audiences, and an Olympic square or park.
There is also an ambition for a major Olympic festival event in the city, along with a campaign to bring the Olympic flame to Leicester before the games.
The council wants to make sure the city attracts tourists from London during and after the games.
It is also hoped the Olympics will inspire residents to become fitter and healthier.
Coun Palmer said: "The Leicester Olympics strategy will be a key driver for vital public health priorities, including reducing obesity.
"We will work to ensure the Leicester and Leicestershire business community is positioned to benefit from the 2012 games. We will do all we can to encourage people to stay in Leicester and to visit our city."