Luol Deng is Great Britain's star player
British Basketball is looking into the possibility of hosting the European Championship finals in 2015 or 2017.
Venues including London's O2 Arena, plus arenas in Liverpool, Manchester and Glasgow could form part of any bid.
Performance director Chris Spice said such events had to be targeted "if we are serious about creating a lasting legacy" from London 2012.
No major championships in Olympic sports are yet scheduled to take place in the UK after the 2012 Games.
A bid to host the 2015 World Athletics Championships was abandoned because of the uncertain future of the Olympic Stadium.
And London lost out to the Netherlands recently when a host for the 2014 Hockey World Cups was decided.
Spice continued: "We hope the entire basketball community in the UK will be excited by the prospect of hosting a major sporting event on this scale and look forward to their involvement."
World basketball's governing body Fiba has made it clear that Great Britain must ensure a legacy for the sport in the UK after the Games if the team is to be handed a place in the Olympic tournament.
Any formal bid would need the support of the home nations and there have been early indications that they would back the plan.
"England Basketball strongly supports the initiative taken by British Basketball to obtain UK Sport funding to assess the feasibility of staging the tournament in 2015 or 2017," England Basketball chief executive Keith Mair stated.
"Along with the World Championships and Olympic Games this event ranks as one of the big three of international basketball and would attract a great many visitors along with vastly increasing the profile of the sport in Britain."
Basketball Scotland CEO Kevin Pringle added: "This is another example of the home nations working together for the good of the sport.
London O2 Arena
Liverpool Echo Arena
Manchester MEN Arena
Glasgow Commonwealth Arena
"We all recognise that the potential of hosting either the 2015 or 2017 [event] can only have a positive impact on the sport."
Will Jones, president of Basketball Wales, said: "It is important for the long-term growth that we are continually looking to unearth opportunities for the sport in the UK.
"As one of the home basketball nations, it is imperative that we offer our full support and backing to the prospect of hosting a European Championship.
"We shall continue to work together to ensure a comprehensive feasibility study is compiled."