"[We] would like to believe that these qualities will be transferred to the foreign policy," Matvienko said.
The upper house speaker pointed out that Russia had repeatedly said it was willing to work with any administration.
"We will see what priorities the new US administration will set in their foreign and domestic policy," Matvienko added.
On December 13, US President-elect Donald Trump officially announced he would nominate Exxon Mobil Chairman and CEO Tillerson to be the next US secretary of state. When commenting on Tillerson's nomination, Trump said that he was chosen to "reverse years of foreign policy blunders and disasters."
Tillerson, who in 2013 was awarded the Russian Order of Friendship and whose oil company is involved in multiple projects in Russia, may face stark opposition at the confirmation process in the US senate over his friendliness toward Moscow.