The tabloid says that Mr Blair will then step down as Prime Minister on July 26, 2007.
The Sun, which claims to be the UK’s biggest selling daily newspaper, supported Labour at the last general election in May 2005.
The prime minister has faced increasing pressure from MPs within his own party to set a date for his resignation to put an end to increasingly damaging in-fighting within his party.
According to The Sun, which did not detail its sources, Mr Blair and a close circle of advisers are working on the details of the exact timing of his resignation.
The newspaper also reported that the prime minister has told only a handful of his closest staff that he will step down at the end of July.
The Sun also reported that the resignation could be brought forward by a week if the party suffers heavy losses at the Scottish and Welsh assembly elections next May.
Mr Blair, who came to power in 1997, has said he will step down before the next general election, due May 2010 at the latest.
But the pledge has turned against him, fuelling increasing turmoil within his own party about who will succeed him and when.
Chancellor Gordon Brown has long been the frontrunner as successor, but his rise to power will still have to go before a Labour Party vote.
Pressure mounted further on Tuesday after a leaked memo set out his "exit strategy."
The sense of urgency was also bolstered by media reports that Labour MPs are circulating at least one letter calling openly for him to go.