The Future of Britain conference, due to take place at the end of June, is billed as a forum to discuss centrist political ideas.
Former prime minister Mr Blair will address the gathering and organisers are said to be ‘desperate’ for Mr Macron to attend, according to Politico.
Key participants are reported to include US economist Larry Summers, financial journalist Martin Lewis and former Scottish Tory leader Ruth Davidson.
An advisory board will feature former Tory Cabinet ministers Rory Stewart and David Gauke, who were kicked out of the party by Boris Johnson over Brexit.
Ex-Labour MPs Angela Smith and Luciana Berger, former Times columnist Phil Collins and broadcaster Trevor Phillips are also said to be on the board.
There is also a bid to involve David Miliband, the former foreign secretary, to talk about Britain’s place in the world, according to the website.