In his state of the nation address on Wednesday, Medvedev proposed extending the presidential term from four to six years, which Vedomosti said was part of an arrangement devised by first deputy head of the Kremlin staff Vladislav Surkov.
The paper said, citing the Kremlin source that under the arrangement Putin's successor needed to amend the Constitution to secure a longer term in office for Putin and to carry out unpopular social reforms. The source told the paper that Medvedev may resign citing changes to the Constitution, leading to presidential elections being held next year.
Vedomosti said Putin could then rule for two six-year terms, from 2009 to 2021.
"There are no reasons why Putin should not return as president next year as the current president's term is not set to expire in 2009," the premier's press secretary Dmitry Peskov told the paper.
Another source close to the Kremlin quoted by the paper said Putin had already started his election campaign.
The premier has launched a personal website and is expected to lay out his manifesto as leader of the ruling United Russia party at a congress in November, following which he will broadcast a video link with the nation, the practice he resorted to as president.
Political analysts and business have been playing a guessing game since Medvedev's election win in May trying to work out who is really in charge in Russia, the president or premier.
A senior United Russia member quoted by the daily said the proposal to extend the presidential term, coupled with the increase in the parliamentary term to five years, was the beginning of constitutional reforms designed to turn Russia into a parliamentary republic.
A source in the presidential administration said the amendments could be approved next year, the paper reported.