According to the report, representatives of the two countries are discussing the exchange 33 for 33 people except for director of RIA Novosti Ukraine, Kyrylo Vyshynskyi.
The press was not told if there was Ukrainian film maker Oleh Sentsov on the lists.
According to the report, Verkhovna Rada Human Rights Commissioner (Ombudsperson) Liudmyla Denisova is already in Russia.
Earlier, Russian mass media said the two countries could conduct the exchange before late August.
In July, the Presidential Office suggested exchange of Sentsov for Vyshynskyi.