The move is aimed at reassuring so-called "aspirational" parents that Labour is the party of high standards, after last week's backlash against health spokeswoman Harriet Harman's decision to send her son to a selective grammar school.
But fast-tracking is also regarded with suspicion by teaching unions - and much of the Labour Party - for promoting selection within schools rather than between them.
John Sutton, general secretary of the Secondary Heads Association, said: "No one seems able to get away from talking about our most able children. I cannot for the life of me see what this will do for middle-ability children, who are most failed by the present system."
Mr Blair has rewritten a speech on social policy, to be delivered today to a church audience at Southwark Cathedral, south London, to focus on education. His aides said this reflected his conviction that the furore over Ms Harman's decision can be turned to his advantage.
Informal opinion polling confirmed that "people are more concerned about where they send their children to school than where Harriet sends her children", they said.
Mr Blair's speech will outline plans for incentives for the best graduate teachers to go to "sink" inner-city schools. Mr Sutton dismissed this as "a diversionary statement", saying the "social priority area allowance" was tried in the 1970s and "it didn't work".
Mr Blair will say nothing about existing selective schools, except to insist that: "The real issue is not selection in 160 schools, it is standards in 25,000 schools serving seven million children".
David Blunkett, Labour's education spokesman, last week expanded on party policy - that the fate of selective schools is a matter for "local agreement". He said the parents of children in all local primary schools would be balloted.
Tory attempts to reintroduce selection, as in Solihull in the mid-1980s, have always been emphatically rejected by parents - because at least three-quarters of children would fail selective exams. The outcome of ballots on selective systems already in place is harder to predict.
In today's speech, Mr Blair is expected to remind the Prime Minister of his statement two years ago that, although the top 15 per cent of schools are "equal to anything you will find anywhere in the world", the other 85 per cent "frankly are not".
He will also highlight a eport by Geoffrey Holland, former permanent secretary at the Department for Education,which said a 30 per cent improvement could be achieved without extra resources.
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