"I will make my position clear next week. I will say something definitive then," Blair told breakfast show GMTV.
Blair said last year that he would resign by this autumn and it has long been thought he would announce his departure soon after reaching Tuesday's milestone of 10 years in power. Blair's Labour Party was elected on May 1, 1997, ending 18 years of Conservative rule.
Blair said Treasury chief Gordon Brown - his longtime friend, rival and likely successor - would make "a great prime minister."
"One of the things I very much hope will be part of the legacy of the government is the strongest economy in the Western world which he has been responsible for," Blair said. "I have always said about him that he would make a great prime minister and I believe that."
Later, in a speech to Labour supporters in Edinburgh, Scotland, Blair appeared to further endorse Brown - who is Scottish - to take over when he leaves.
"Within the next few weeks I won't be prime minister of this country," Blair said. "In all probability, a Scot will become prime minister of the United Kingdom."
Blair was campaigning in Scotland, one of the key battlegrounds in local elections on Thursday. The pro-independence Scottish National Party is polling well, and Blair's Labour party is fighting to keep control of the Scottish Parliament in Edinburgh.
The face of USA's First Lady Melania Trump after her handshake with Russian President Putin has received a lot of attention in social media
The Ukrainian government refuses to abode by its obligations, rejects a peaceful resolution of the conflict, and disregards its own people, the president said