The former prime minister said the British people “have the right” to change their minds on the result of the June referendum.
And he insisted that Remain supporters would keep up the fight to warn voters about the “costs and consequences” of Brexit.
Speaking to French radio station Europe 1, Mr Blair acknowledged that a decision to remain in the EU did not currently look “probable”.
But he said there were several factors that might shift opinions, pointing to the fall in the value of sterling, damage to the financial services industry and car manufacturing and an expected reduction in foreign investment in the UK.
Asked whether it was possible that opinion would move sufficiently to avoid Brexit, Mr Blair - speaking in French - responded: “At the moment, today, it is not probable, but the debate continues and I believe it is possible.”
He rejected suggestions that Remain supporters should simply accept the 52%-48% referendum vote in favour of Brexit as the final word on the issue.
“Who made a rule that we have to stop the debate now?” he said.
Asked whether the campaign to stay in the EU could continue and British people could still change their minds, he said: “We have the right.”
Mr Blair said that Prime Minister Theresa May had to stick to her position that “Brexit means Brexit” in order to preserve the unity of the Conservative Party, but added: “For the rest of us, we are free to have a debate.”
There was currently “confusion” over the way forward because “we do not know the terms of Brexit”, said Mr Blair.
“We have done something rather bizarre with Brexit,” said the former Labour leader. “It’s like moving house without having seen the new house. We have made an agreement to exchange, but we don’t yet know the terms of Brexit, we don’t know the costs and the consequences.”
He added: “There will come a moment when we have had the negotiations and we can see the terms we are being offered by the rest of Europe and we will be able to say that it is a good idea or perhaps that it is a bad idea with major consequences.”