West Midlands MEP Bill Etheridge said the suggestion of a team comprising EU members was the subject of “serious” debate behind closed doors in Brussels and Strasbourg.
The UKIP MEP said Brussels chiefs would like like an EU team enter the 2036 Games, the 100th anniversary of the Berlin tournament, which was opened by Adolf Hitler.
Mr Etheridge said the move was out the latest attempt by EU leaders to “destroy national identity”.
And he claimed it was partly driven by envy of Great Britain’s success in Rio and London.
He said: “There have been quite a lot of conversations about it among other MEPs and it was being taken quite seriously by some of them.
“They were using the word solidarity, which tends to be code for ever closer union.
“It speaks to their plan to create a united states of Europe.
“I’m almost certain there was some jealousy at Britain’s success in 2012 and 2016 and they want a piece of our success.
“It’s a crazy EU effort to destroy national identity.”
The secret discussions have only been held informally so far and no official approach has been made to tournament organisers, The Telegraph reported.
Team GB finished the 2016 Rio Games second in the medal table behind the US, having won 27 golds.
Germany came fifth with 17, France seventh with 10 and Italy ninth with eight golds.
British success followed the 2012 Games where 29 gold medals were won on home soil, the highest of any European nation.
News of trying to bring the bloc’s members together for the world’s biggest sporting event comes at the end of a year where key Brussels figures have launched plans for a much tighter union.
European Commission President Jean Claude-Juncker and French leader Emmanuel Macron have led the charge, with proposals for a joint budget and EU army.
In a landmark speech in September, Mr Juncker set out a vision for a united states of Europe.
He said he wanted more financial unity across the bloc, headed by a new finance ministry while transforming the eurozone’s bailout powers into a European Monetary Fund.
Mr Juncker also wants every member state to join the Euro.
Brexiteers pointed to the speech as a demonstration of why the UK was right to leave the bloc.
Among high-profile critics of the approach was ex-UKIP leader Nigel Farage who raged: “I think Europe is about diverse nations and cultures.
“It makes it the most fascinating continent on Earth and provided that all democratically run, they will be at peace.
“I’ve seen time and again the peoples of Europe in referendums reject deeper integration, reject the European constitution just to be wilfully ignored by Brussels who have either made them vote again or ignored them and gone round the back of them.”