During a speech later he will say the vote to leave the EU puts the disintegration of the UK back on the table.
The former Labour PM will also argue that people should be able to change their minds on the EU referendum since they voted without knowing the terms of departure.
First Minister Nicola Sturgeon said a second independence referendum would be “very likely” following the EU plebiscite last June, which saw Scots opt to remain while the UK as a whole voted to leave.
Mr Blair, who was UK prime minister between 1997 and 2007, will say in his speech to the campaign group Open Britain that those pushing for withdrawal from the EU “always wanted a hard Brexit”.
He will announce his “mission” to persuade Britons to “rise up” and change their minds on leaving the bloc.
He will also say: “In addition to all this, the possibility of the break-up of the UK - narrowly avoided by the result of the Scottish referendum - is now back on the table but this time with a context much more credible for the independence case.”
At the weekend, former first minister and SNP MP Alex Salmond suggested that a decision on whether to hold a new independence referendum could come within weeks.
He said the UK government’s response to Scottish plans to protect trade with Europe would be crucial.
Mr Salmond, the SNP’s international affairs spokesman at Westminster, said a rejection of the plans would probably result in an autumn 2018 referendum.
It has also been reported that Brussels is prepared to do a separate Brexit deal with Scotland.
According to The National, leaked European Parliament negotiating documents state that senior EU figures are ready to explore how a “Norwegian-style” arrangement for Scotland could work. However, Prime Minister Theresa May and her ministers have said that any Brexit deal has to be done “under a single banner”.