The ex-prime minister said there could be majority support for a new EU poll if Parliament ended up "gridlocked".
He urged Theresa May to "facilitate" the process by "running all options" by MPs first, including Norway and Canada-style alternatives as well as her deal.
But Labour frontbencher Angela Rayner says another referendum could increase division in the UK.
The shadow education secretary told the BBC's Question Time that holding a further Brexit vote would "undermine democracy".
"People made the decision and you can't keep going back saying, 'Would you like to answer it a different way?'"
And Hilary Benn, the Labour MP who chairs the Commons Brexit committee, has also distanced himself from calls within his party for another vote, telling BBC Radio 4's Political Thinking podcast that politicians have a "responsibility to give effect to the result of the last referendum".
But he told presenter Nick Robinson: "If the deal goes down… it may be that the prime minister decides, 'Well, I'm taking my deal to the country.'" [...]
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Related article on BBC: Theresa May condemns Tony Blair's new Brexit vote call
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