“It’s not too late until we leave,” he told Today.
The ex-Labour leader said the “sensible” option was to “take a final decision” once the terms of the deal have been set out.
He added: “I think it is more likely we can stop it now than it was a few months ago.”
Mr Blair made the comments as he signalled Labour MPs should rebel against Jeremy Corbyn on Brexit if they thought it was in the national interest.
With just one year to go until Britain formally quits the European Union, the former prime minister said MPs must vote with their conscience.
He told The Independent: “I think all MPs have got a responsibility to do what they think is right and that’s why what I was urging MPs to do, whether Conservative or Labour, is vote according to what you genuinely believe.
“This is the most important decision since the Second World War and it’s going to decide the destiny of the country for future generations. Do what you think is right, this is one moment surely to do that.”
Mr Blair also called on Prime Minister Theresa May to give MPs a free vote on the issue.
“What I think would be more sensible for the Government, is actually to give MPs a free vote, because it is such a huge question and it’s a question where opinion is divided everywhere,” he said.
“It’s one of those rare occasions and I’m aware I’m saying this as a former prime minister that would have obviously wanted in general terms the whips to be active on big issues of the day, but I think this is an issue that is unlike any other.
“I think all MPs whether they are Labour or Conservative should on this issue go with what they believe.
“I think that on this issue, Parliament is the only thing that can allow this issue to be handled in the right way, and by the right way I mean before we leave, before we take the irrevocable step of leaving, we’ve got to know what we’re getting in place of European Union membership.
“If I’m right and the Government is going to avoid giving us that choice, before March 2019, we’ve got to force it on to the agenda and keep it there.”
The intervention came as some pro-Europe Labour MPs reacted angrily to reports shadow foreign secretary Emily Thornberry said the party would probably vote in favour of Mrs May’s Brexit deal in the autumn.
Ms Thornberry was reported to have said the PM would return with such a “blah, blah, blah” deal it would probably pass the six tests Labour had set for a Brexit agreement, stating: “We have our six tests. If you hold up blah, blah, blah, to six tests, you’ll probably pass it.”
Chuka Umunna, who supports the pro-Europe campaign Open Britain, said: “It is extraordinary and unacceptable that the shadow foreign secretary seems to be suggesting that some ‘blah blah’ from the Government will be enough to secure Labour’s support to write the Government a blank cheque for Brexit.
“The public will rightly take a very dim view of the Labour frontbench joining arm in arm with the likes of Jacob Rees-Mogg and other Brextremists to vote for a Brexit which will cost jobs, damage living standards and leave our public services with less investment.”
A Labour spokeswoman said: “Emily made clear, as we have done for more than a year now, that the Government needs to deliver a deal which meets our six tests, in particular by explaining how we will maintain current arrangements on the Northern Ireland border, and ensure all UK firms maintain the current benefits of access to the single market and customs union.”