Forty eight per cent of referendum voters nominated to remain while 52 per cent opted to leave.
"The odd thing about the referendum was we knew what we were getting out of, (but) we don't know what we're getting into," Blair said.
"As that becomes clear, if it's clear that these terms are bad for us, if we have major parts of business and the financial sector saying look this is not a good deal for us, if people start to worry about their jobs, we should just keep our options open."
Blair told the BBC that many 'leave' voters felt "disenfranchised" since the Brexit vote.
"There is going to be a negotiation of extraordinary complexity where there are a thousand devils in every detail. Those we used to call "our European partners" are, unsurprisingly, divided and uncertain themselves," he said.
"If the will of the people shifts, why shouldn't we recognise that?
"We our sovereign. Let's just keep our options open."
Both prime minister David Cameron and Labour leader Jeremy Corbyn have ruled out a second EU referendum.
Blair told Radio 4 the case for leaving the EU had "crumbled" despite the Brexit vote having been of "seismic importance".
He said Prime Minister David Cameron's resignation and the leadership contest meant the focus would be on appealing to Conservative Party members rather than the country's national interest.
He said the government should engage now with other EU countries to see what room there was for manoeuvre, stressing the continuing importance of Cameron's role in this, rather than waiting for the outcome of the Tory leadership race.
"If ... once we look through the rest of our European partners, we start to see where there is a possible route for compromise, my point is this: We are sovereign. Let's just keep our options open," Blair said.
"Yes right now, it's clear, we're leaving. But we don't know what we are going to."
Blair said Britain had "diminished" its place in the world and would have to "fight to get it back".
"My point is why do all this unless there's some huge gain we can see on the other side, which right now we can't," he said.