Miliband, who has been nicknamed "Red Ed" by some in the press and is much less sympathetic to Blair than his brother David, who he defeated in the 2010 Labour party leadership election.
Blair, who won three general elections as party leader after taking the party in a centrist direction, will give a speech on Monday marking the 20th anniversary of him becoming Labour leader, outlining the need for the party to fight elections on the centre ground.
“He will not want to take a pop at Ed, and he will want to show commitment to the Labour party at the next election,” an ally of Blair's told The Sunday Times (£).
Blair will give the speech at the left-leaning think tank Progress.
He came out all guns blazing against Ukip, after the eurosceptic party triumphed at the European elections in May, dismissing the notion the major political parties should try to reclaim support lost to them by talking tough on Europe.
When asked what Miliband should do, Blair said: "I would advise him to stay firm.
"It is not as if yielding to that pressure from Ukip has actually done the Conservative Party any good at the present time.
"For the Labour Party, if it decides to follow Ukip either on its anti-Europe platform or even worse franky on its anti-immigration platform then all that will happen is that it will confuse its own supporters and it won't actually draw any greater support."
He added: "The way to deal with Ukip is to stand up and take them on. What they are putting before people is a set of solutions that anybody, who analyses where a country like Britain needs to be, knows are regressive, reactionary solutions that would make the problems of the country worse not better."
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