The Gunners are on the verge of qualifying for the tournament for the 16th consecutive year after beating the Turks 3-0 away in the first leg last week.
"It is really important to us," Vermaelen told the club's official website. "The club belongs there, as you can see from the number of times we have qualified, and for players there is nothing better than to compete in it.
"It's the highest level of the sport, and the place you want to be when you're a young kid. So it's vital to see things through, and I am confident in our team."
Vermaelen will miss Wednesday's match against Fenerbahce as he recovers from a back injury.