Gorbachev, who recently held a telephone conversation with U.S. President Barack Obama and a meeting with Russian President Dmitry Medvedev, said in an interview with La Republica that the two former Cold War foes would look to tackle arms control and missile defense shield differences.
"There are grounds for optimism so far," he said.
His statement echoes opinions by Russian officials that Obama is less determined to pursue his predecessor George Bush's plans for a missile base in Poland and a radar in the Czech Republic. Moscow has fiercely opposed the plans as a security threat.
Speaking about a meeting with Medvedev last week dedicated to the recent shootings in Moscow of a lawyer and a journalist with the Novaya Gazeta newspaper, Gorbachev, who is a co-owner of the paper, said the president had not planned "to make any political statements, but wanted to talk about a fact that had shocked him."
Lawyer Stanislav Markelov was shot dead on January 19 in downtown Moscow. Novaya Gazeta journalist Anastasia Baburova was also wounded in the attack and died a few hours later in hospital.
At least five Novaya Gazeta journalists have been killed since the paper was founded with money donated by Gorbachev in 1993, including Anna Politkovskaya, who had gained international recognition for her coverage of human rights abuses during the Kremlin's antiterrorism campaign in Chechnya.
Gorbachev said the authorities should respond more energetically to what he described as ultra-nationalist attacks.