Blair, a strong supporter of Britain remaining with the European Union, said "It is absolutely necessary that it doesn't happen". But he called Brexit the biggest political decision since World War II. But pressed in interviews, he declined to identify the sources who had indicated which leaders he was referring to.
How this could be achieved is a different matter; Mr Blair thinks it can form part of negotiations.
In his article, Blair outlined his views of the current situation in Britain.
"We think we can negotiate access and that will protect jobs and will protect the economy". We are now the slowest", he said, "The worldwide investment community is negative on us. Incomes are stagnating. The global reputation of Britain is rapidly losing altitude.
He described Britain as feel like a country which has lost its footing and is stumbling, but seemingly with no choice but to stagger on.
Mr Blair suggested the election of Emmanuel Macron in France "changes the political dynamics of Europe" with European Union member states now likely to integrate more closely. So I favour a three-year transition, starting in March 2019, in which we join the European Free Trade Association and become temporary members of the European Economic Area like Norway.
Media playback is unsupported on your device Media caption Jeremy Corbyn"I hope he has looked very carefully at our manifesto
Blair served as British prime minister for 10 years from 1997, winning a landslide victory that kept the Labour government in power for years.
Mr Blair reiterated his belief that abandoning the single market would be "damaging" for Britain's economy while predicting that Europe "will comprise an inner and outer circle" in the coming years.
The former prime minister said in an article that the election of Emmanuel Macron as French president had opened up the prospect of real change in Europe, which could enable Britain to stay in the bloc.
He says: "Given what is at stake, and what, daily, we are discovering about the costs of Brexit, how can it be right deliberately to take off the table the option of compromise between Britain and Europe so that Britain stays within a reformed Europe?"
Blair told Sky News Saturday: "I think it's absolutely necessary that it (Brexit) doesn't happen because I think every day is bringing us fresh evidence that it's doing us damage economically, certainly doing us damage politically".
He noted that French and German voters share some of the concerns expressed by their British counterparts, particularly on immigration and concerns about the freedom of movement.
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We have increased the numbers here in the city because what we're simulating here today is an global terrorist threat. We have to make sure that we are ready to respond to those incidents. "That said, this work goes on relentlessly".