"A total of 80% of respondents planning to vote will back Dmitry Medvedev," said head of the Levada pollster, Lev Gudkov.
Meanwhile, some 55% of respondents believe that the elections are a foregone conclusion and the idea that the election is a competition among the candidates is just a pretense, Gudkov added.
Russia's first deputy prime minister, Medvedev, was publicly backed by Putin as his successor in mid-December, and was later nominated by the ruling United Russia party as a presidential candidate for the country's crucial elections.
Given Putin's popularity, his endorsement of the first deputy premier is likely to guarantee Medvedev the presidency. Putin has also said he will accept the post of prime minister if Medvedev becomes president.
Levada also predicted Communist leader Gennady Zyuganov would come second with 11% of the votes, and ultra nationalist Liberal Democratic Party leader Vladimir Zhirinovsky will be third with 9% of the votes.
The leader of the tiny pro-Western Democratic Party, Andrei Bogdanov, is forecast to receive just 0.5% of the vote.
Gudkov also said that voter turnout on March 2 would be around 75%.
The poll was conducted on February 8-11 among a sample of 1,600 respondents, with an error margin not exceeding 3 %.