Earlier, a diplomatic source told Sputnik Russia has not yet received any invitation from the United States to discuss the fate of the treaty.
Trump is considering former nuclear negotiator Richard Burt, Treasury Department official Marshall Billings and former national security adviser Stephen Hadley for the role, the report said citing US officials.
Trump has come under increasing political pressure to preserve New START which came into effect in 2011 and expires next February. The treaty limits the United States and Russia to 1,550 deployed long-range nuclear warheads and 700 long-range delivery vehicles.
Russia has repeatedly stated its readiness to extend the New START treaty without any preconditions, but the United States continues to be undecided about an extension.
In January, Russian Foreign Ministry issued a statement, noting that Russia will take all necessary steps in order to ensure its security if the United States moves to terminate New Start.