If Rublev were to come through that encounter, he would well run into the red-hot Ilya Ivashka.
Ninth seed Anett Kontaveit also reached the quarter-finals in Moscow with a 6-1, 6-4 win over Andrea Petkovic in just 69 minutes.
The Serb has landed in a packed quarter featuring former Grand Slam champion Marin Cilic and an in-form Tommy Paul.
The 2019 champion will, in all likelihood, face seasoned Frenchman in his opening match.
There is another site called bet365 that will also broadcast the tournament from their site.
Open champion Daniil Medvedev has withdrawn from next week's Kremlin Cup in Moscow in order to focus on the remainder of the season, the Russian said in a statement on Friday.