The Crescent-Stars recorded a 2-1 victory over Austria in the round of 16 to advance to the final eight, and a win over Netherlands would see them take on either Switzerland or England in the semi-finals.
Calhanoglu missed the clash with Austria through suspension, but he will be back in the XI against Netherlands, and the Inter Milan attacker has previewed the enticing contest.
"Everyone is very happy. The games went well for us. We are exactly where we want to be in the competition," Calhanoglu told UEFA's official website.
"We hope to get another victory. This is our biggest dream. We always speak about what we believe in. There is nothing we cannot achieve. Nothing is impossible.
Turkey reached the semi-finals of Euro 2008
"In fact, before the Austria match, we said we wanted to reach [the quarter-final] and we did just that. We want to get on the field with the same mindset.
"I'm playing with Stefan [de Vrij] and Denzel [Dumfries] at club level. I'm really happy to be able to see them, as it's been a month since we've last seen each other. It'll be good but I hope to be on the winning side.
"Since 2013, I've learned a lot from my captains. They made a significant contribution to me. I'm really grateful to them because we've worn the same jersey and they've always told me that I'd be the captain of this team one day.
"It's a nice environment to be in. Being the captain of the national team has always been my dream, to be honest."
Calhanoglu will return from suspension against Netherlands
Meanwhile, Turkey assistant manager Daniele Russo added: "We have known him since his time at Milan [from 2017] and are aware of what a leader and character he is.
"There is no need to mention what an incredible player he is. He is also very good at protecting the young players; they are talented, but some things are not easy in a tournament where you play every four days. We thank our captain for this."
Turkey will be without three players through suspension on Saturday, with Orkun Kokcu and Ismail Yuksek both picking up milestone bookings against Austria.
Meanwhile, Merih Demiral has been handed a two-game ban by UEFA for his celebration after scoring his second of the match against Austria last time out.
Demiral celebrated with a 'wolf salute', which is associated with Turkish right-wing extremist movement the 'Grey Wolves', and he has now been hit with a two-game suspension, although the Turkish Federation have appealed to CAS.