Media reports have speculated that Dmitry Medvedev, recently promoted to the post of first deputy prime minister in charge of four multibillion-dollar national projects to raise living standards, and Defense Minister and Deputy Prime Minister Sergei Ivanov, Putin's former KGB colleague, could possibly be candidates in the 2008 presidential campaign.
"I have stated repeatedly that I am indifferent to this," Medvedev said.
He was responding to a question from journalists in the lobby of the lower house of the Russian parliament.
"This neither helps nor hinders me. I have a modest task - to perform my duties and fulfill the assignment that the president gave me. And this is what I will do," he said.
Asked whether the Russian Constitution, which limits a president to two consecutive terms in office, could be amended, he said: "This is not a question for the government to decide."
He said the Constitution should be a stable document, but that it would be wrong to treat it dogmatically.
"But this does not mean the Constitution must change. Any constitution, including an economic one, should change as rarely as possible," he said.
Sergei Ivanov earlier denied media reports he intended to run for president.
Putin said in mid-June the name of his successor will become known as the presidential election draws nearer, but he said it was up to the Russian people to choose a president.
The prospect of Putin staying in power for a third presidential term after his current term in office runs out in 2008 has also been widely debated in Russia, although the president himself has repeatedly said he will not run again. He said the Constitution bans anyone from having more than two consecutive terms as president.
Putin also said he was against amending the Constitution to allow a third consecutive term. Another possibility that has been advanced is that Putin could take up the presidency again in 2012, as the Constitution specifies only consecutive terms in office, without imposing a limit on the total number.
Despite criticism in the West over alleged democratic backsliding, Putin remains hugely popular at home, where he is credited by many for bringing relative order, and for attempts to reconcile the Communists and Democrats following the upheavals of the 1990s.
