The two La Liga giants both secured their progression from the last-16, with Barca seeing off the challenge of Celta Vigo while Madrid shot down Numencia.
And, speaking ahead of today's draw, which is schedule to take place at 13:30 South African local time, Valverde admitted he would prefer facing their bitter rivals at a later stage in the tournament.
“I don't want to be drawn Madrid, but I have to say that so we can play them later in the competition,” the Coach said after the game.
When asked about the impact of Ousmane Dembele, who recently returned from a lengthy injury layoff, Valverde said: "He's taken an important step. When he plays, something always looks like happening because of the pace and technique he has.
“He's different to the others. He needs time to adapt, but he's dared to do more. Messi? He's fine, we were on top and there's an important match on Sunday."