By Bridget Kendall
Diplomatic correspondent, BBC News
Mr Putin first came to power in 1999
Russian PM Vladimir Putin has given the clearest indication yet that he might run again for the Russian presidency.
Mr Putin did not commit himself, but hinted that he is thinking of coming back in 2012 when President Dmitry Medvedev's current term expires.
The two leaders would not compete, but Mr Putin said: "We'll reach an agreement."
He was speaking in Moscow to the so-called Valdai Club of foreign academics and journalists.
The club holds a series of briefings with senior Russian politicians every year.
Mr Putin tried to downplay any suggestion of rivalry, insisting that whatever happened would be as the result of a deal which they came to jointly.
"Did we compete against each other in 2007 [before the last presidential election]?... No, we didn't. And so we won't in 2012 either. We'll reach an agreement," he said.
President Medvedev (l) took over from Mr Putin in 2007
"We're people of the same blood, with the same political views.... When it comes to 2012, we'll work it out together, taking into account the current reality, our own plans, the shape of the political landscape, and the state of United Russia, the ruling party."
As ever sensitive to how his behaviour might look to critical outsiders, Mr Putin drew an analogy with the UK, defending the notion of one politician handing the baton of leadership on to a close collaborator without wider consultation.
"When my friend Tony Blair retired, Gordon Brown immediately became prime minister," he said.
"Were the people of Great Britain consulted on this? No, there was a change of leadership in the country and it was the two of them who decided it."
"When my term expired," he went on, "I supported Dmitry Medvedev because I thought he was the best person to be the country's leader, and I was right."
And now, he seemed to be hinting, the time might come when President Medvedev would be asked to return the favour.
If Mr Putin were to stand again, it would probably come as little surprise to most Russians.
His popularity in opinion polls is helped by his high visibility in Russia, which he seems to make a high priority.
Mr Putin had a high profile even during his summer holiday
This summer he even posed bare-chested for a photo shoot while on an adventure holiday.
His promise in front of Russian TV cameras, to raise pensions by 30% this December as part of a wider pension reform plan, will no doubt do no harm to his reputation among many older Russian voters.
What remains to be seen is how President Medvedev views the succession question.
Russian analysts continue to puzzle over how he really works "in tandem" with Mr Putin and whether at times they even deliberately play a joint game of "good cop-bad cop" to reach different audiences, or whether their collaboration hides tensions between two camps which represent different viewpoints on where they think Russia is heading.
On Thursday, President Medvedev published a startlingly bleak article on a Russian website, lamenting its totalitarian past, weak democracy, ineffective economy, endemic corruption and a "pandemic" of alcoholism.
He laid out what he said was a personal ambition to transform Russia into a hi-tech knowledge economy, but pointedly warned that '"influential and corrupt" officials opposed this and would try to stop it.
But whatever the real relationship between Russia's president and prime minister, Mr Putin's comments remain potentially significant.
In the last year the Russian presidential term has been extended to six years.
So if Mr Putin were to come back as president in 2012 and serve the two new terms he would then be eligible for, he could in theory preside over Russia until 2024.
Since he first came to power when President Boris Yeltsin made him his successor in 1999, that would mean the Putin years in Russia might extend to a quarter of a century.