Richard Edgar Pipes, professor of Russian History at Harvard University, told CNBC that there was a danger that prolonged weakness in the economy could harm Putin, whose popularity among the Russian electorate has been waning for some time.
"Around 52 percent of Russians do not want him to run for presidency again, which is astonishing," Pipes told CNBC at a meeting of the Russia Forum, an annual business and investment conference, held in Moscow.
"If the economy begins to weaken there will be a demand for big change. Whether it's liberal or anti-liberal depends on whoever promises the improvement in the economy," he told CNBC on Thursday.
(Read More: Putin Threatens to Sack Officials Over Social Spending)
According to Pipes, foreign investors who were apprehensive about Russia as a "safe" place to invest would be more receptive to a Russia with Medvedev at the top.
"Foreign investors are loathe to invest in this country because they are not sure the investment is good. Investors are [easily scared]and they like to invest in Switzerland or the U.S. because they like to guarantee that their investments are safe. If Medvedev were to become the top man in Russia, investments would flow more readily than under Putin," he said, adding that their styles were very different.
"I think Putin is more autocratic and Medvedev is more liberal. Medvedev has said things that Putin would not have said. The rift maybe about more authority or less authority and more democracy or less democracy. Medvedev conforms to the western idea of a president," Pipes said.
Russia's industrial output was flat in the first quarter and the world's largest oil producer has been hit by a decline in oil prices.
The economy's decline has prompted fears of another recession with some criticizing the fiscal rule brought in under Putin that bases spending plans on the long-term average oil price and caps the budget deficit at one percent of gross domestic product (GDP).
In a sign the government could change its stance, Medvedev said the government would consider other stimulus measures to push growth closer to the target rate of 5 percent this year, if the economic slowdown continued.
His comments came after President Vladimir Putin threatened to fire senior officials if they did not follow his orders over social spending, prompting media speculation that Putin's comments were a thinly-disguised attack on Medvedev's leadership. On Wednesday, the Moscow Times newspaper reported that there could be a cabinet reshuffle soon.
Russia's next central bank chief, Elvira Nabiullina, who takes over in June, said that Russia's economy was performing below its potential level of 3 to 4 percent growth. But she added the central bank should not sacrifice its main policy goals, such as lower inflation, for the sake of higher economic growth.
"I am against boosting economic growth at the expense of ... inflation," Nabiullina told reporters late on Wednesday. Russia is fighting a battle against inflation which rose to 7.3 percent in February, up from 3.7 percent a year before.
By CNBC's Shai Ahmed and Holly Ellyatt; Follow them on Twitter
Correction: An earlier version of this story stated that Russia was the world's second-largest oil producer. However, based on recent data from the IEA, Russia is, in fact, the world's largest oil producer, ahead of Saudi Arabia.