The proposal to extend the length of time a president can serve from two consecutive terms of four years to two consecutive terms of six was made by Dmitry Medvedev, the Russian leader, just last week.
Medvedev's declaration marks a watershed in Russian politics.
Ever since it was drafted 14 years ago, the idea of changing the country's constitution has been considered taboo.
Yet Kremlinologists, many of whom have predicted Putin's return as president, regard the constitutional amendment as inevitable.
Once passed, Putin will be allowed to serve 12 years rather than eight.
Existing Constitutional restrictions had forced Putin to stand down in May after completing two consecutive four years terms. He did not go far, however, changing jobs to become prime minister.
Few commentators expect Medvedev to mount a challenge should he be asked to go.
Even so, political analysts have predicted that Putin would wait for Medvedev to serve a full four-year term before replacing him in 2012.
"It is evident that there has been a collapse in the consensus of the Kremlin's elite factions. The situation is deteriorating in such a way that Putin's team has to consolidate power by whatever means it can as quickly as it can," the Telegraph quoted Dmitry Oreshkin, a leading political analyst, as saying.