AP Photo/George Widman
If they pull it off, the debate would be the BBC's biggest event centered around an election since they hosted the "Scotland Decides: The Big, Big Debate" for 7,500 teenagers ahead of the Scottish referendum.
Speaking at Chatham House on Wednesday, Foreign Secretary Philip Hammond said most people will only start paying attention to the EU referendum a couple of weeks before it happens. If he is right, a huge TV debate held on June 21 really could help swing votes in what is going to be a very tight race.
Alongside Johnson and Osborne, who are also the frontrunners to become the next leader of the Conservative Party, The Telegraph reports the BBC also want UKIP leader Nigel Farage, Respect leader George Galloway, Work and Pensions Secretary Iain Duncan Smith, Green leader Caroline Lucas, former Labour Home Secretary Alan Johnson, and Liberal Democrat leader Tim Farron to join the debate.
BBC presenters David Dimbleby, Mishal Husain, and Emily Maitlis will present the event.