The Turkish side qualified for the knock-out stage by finishing above Cluj and Braga (but below Manchester United) in Group H, while their Bundesliga opponents topped Group B above Arsenal, Olympiakos and Montpellier.
In Tuesday's press conference, the Istanbul club’s boss rejected any notion that the German team are inferior ahead of the last-16 first leg.
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"We've been analysing Schalke for some time now," Terim told reporters. "But the media are trying to make them look like a weak team. This is not the case at all.
"These reviews about Schalke certainly hurt us. It doesn't matter how many injured players they have, Schalke are still a great team. They haven't lost a single group match.
"We should be focused. A clean sheet would give us the upper hand before the second leg."
Although the coach stressed Schalke’s strengths, he also accepted the knock-out draw was kind to Galatasaray, as Group H winners United were pitted against a more formidable side in Real Madrid.
"We were pleased to draw with Schalke but so were they," Terim continued. "If we knock Schalke out, the media would say that we've beaten an easy team. But we do not care about those words. We absolutely do not underestimate Schalke."
As well as building up his side’s opponents, Terim was keen on stressing that his own team possess a wealth of dangerous players, including their star January signings.
"We are in a transition period now after Wesley Sneijder and Didier Drogba," he admitted. "We will try to get the best out of them.
"Drogba has had just 30 minutes of playing time with us. I will decide if I'm going to include him in the starting line-up, tonight or tomorrow morning. The experience levels of both Drogba and Sneijder will boost our chances.
"Sneijder is a very clever football player. We're pleased that he's settled into the team so soon. He will get much better as time passes by.
"The European press have highlighted Didier Drogba, Wesley Sneijder and Burak Yilmaz, but [midfielder] Selcuk Inan deserves to be mentioned. He's very important for us."
Terim refused to dwell on Schalke’s star striker Klaas-Jan Huntelaar, who is still recovering from an eye injury, and reiterated the club’s entire team need to be monitored closely.
"I don't know if Huntelaar will play or not but it's not about certain names," the coach concluded.
"This team has some quality players. They have topped the group that had Arsenal in it. We shouldn’t be focusing on individuals. They're dangerous as a team."