The term perestroika, meaning restructuring, was used by Gorbachev in the late 1980s to describe a series of reforms that abolished state planning in the Soviet Union.
In an interview with Italy's La Stampa published on Friday, Gorbachev said President-elect Barack Obama needs to fundamentally change the misguided course followed by President George W. Bush over the past eight years.
Gorbachev said that after transforming his country in the late 1980s, he had told the Americans that it was their turn to act, but that Washington, celebrating its Cold War victory, was not interested in "a new model of a society, where politics, economics and morals went hand in hand."
He said the Republicans have failed to realize that the Soviet Union no longer exists, that Europe has changed, and that new powers like China, Brazil and Mexico have emerged as important players on the world stage.
He told the paper that the world is waiting for Obama to act, and that the White House needs to restore trust in cooperation with the United States among the Russians.
"This is a man of our times, he is capable of restarting dialogue, all the more since the circumstances will allow him to get out of a dead-end situation. Barack Obama has not had a very long career, but it is hard to find faults, and he has led an election campaign winning over the Democratic Party and Hillary Clinton herself. We can judge from this that this person is capable of engaging in dialogue and understanding current realities."
Former Russian oligarch Mikhail Khodorkovsky, founder of now defunct Yukos oil giant, who is in prison on fraud and tax evasion charges, also used the word perestroika in discussing the future course of the Obama administration.
In an article published in the business daily Vedomosti on Friday, Khodorkovsky said Obama's election win was not merely another change of power in a separate country, but was important for all states.
He said that, "being a liberal himself, he thinks that the world will take a left turn," and that "a global perestroika would be a logical response to the global crisis."
"The paradigm of global development is about to change. The era inaugurated by Ronald Reagan and Margaret Thatcher 30 years ago is over."
He said decisions in neoliberal economies had been made mainly by supranational institutions and transnational corporations.
Khodorkovsky predicted: "Globalization will slow to a crawl, but will not stop. The 'golden billion' of the world's richest people will have to abandon hopes of increasing their wealth, but high consumer standards which developed at the end of the 20th century will be unaffected by the change. The striving for political freedom and open competition of personalities and ideas will not disappear."