Ziyech hopes to start the quarterfinal first-leg tonight at Stamford Bridge.
He told the club's website: "It's a totally different situation from last year, a different atmosphere, a different time.
"They've [Real Madrid] also improved as a squad, with some young players as well, so it's a totally different game than last year.
"We know how difficult it can be against Real Madrid. We played them in the semi-final last year and now we play them in the last eight, and there will be a crowd back. So the motivation will be different, the discipline should be different, but the most important thing is that you must enjoy it.
"Those kind of games – if you don't enjoy them, you'd better choose another sport because these are the games you dream of. It will be a hard game, a physical game, a mind game, but one to enjoy from the first minute to the last."
Of his own form, Ziyech continued: "I've now been playing for a long period – okay, I had a small injury again but it didn't put me off my form. I feel comfortable, I feel good, I feel happy and in that situation the football will come by itself.
"You don't win those kinds of trophies often, so we have it now and we are in the race for another one. We need to give everything we've got to defend it and make sure the cup stays in London."