Real Madrid accounted for Atalanta 3-1 in the Spanish capital on Tuesday, rounding out the tie, with goals from Karim Benzema, Sergio Ramos and Marco Asensio.
Los Blancos had been knocked out at the last 16 in the past two seasons but Zidane is now dreaming about winning the title, along with La Liga where they sit third.
That’s what we’re going to try to do,” Zidane said when asked if Real can win both titles.
“Why not? That’s what we’re here for. Were going to try to do it. Its a big ask, but well give it our all.”
Real are currently third in La Liga with 11 games to play, sitting six points behind rivals and leaders Atletico Madrid, with Barcelona in second.
“Were alive in both competitions and tonight we have to enjoy this, not just because of the goals we scored but particularly because of our performance,” Zidane said.
“When you work on things with the players and they then come off in a game it makes you really happy, particularly when it’s against a team that demands so much of you.”
Elsewhere, Manchester City eased into the quarters with a 2-0 victory over Borussia Moenchengladbach, sealing a 4-0 aggregate triumph.
Early goals from Kevin De Bruyne and Ilkay Gundogan secured the win for City who are among the Champions League favourites.