Rivals Fenerbahce and Besiktas have both beaten Manchester United away from home in European combat.
Now Terim wants his beloved Galatasaray to complete the hat-trick.
"They are our big rivals but I remember Fener and Besiktas both did a fantastic job," he said.
"We have drawn at Old Trafford in the past, but now we hope to follow them. We want to achieve something exactly as our rivals did."
Galatasaray will have a few familiar faces helping them too.
Johan Elmander, Emmanuel Eboue, Milan Baros and Albert Riera are all well known to Premier League supporters.
It means a quartet of Terim's squad will be familiar with such a grand stage, unlike so many of Galatasaray's travelling party.
Indeed, Terim wonders whether a team making their return to the competition after a four-year absence would have been better meeting one of the lesser lights.
"It would have been better to play against Cluj or Braga," he said.
"Then we could have gained more experience.
"Instead we have to play against one of the best sides in the world immediately."
For that is how Terim still regards United, even though Sir Alex Ferguson's men were unceremoniously dumped out at the group stage of last season's competition.
"Manchester United have been so successful in the Champions League for many years," he said.
"I was there when they beat Bayern Munich in the final and they have won many more important games apart from that.
"What happened last season was a surprise but maybe it will just make them even more motivated."
Galatasaray will be backed by 2,500 fans at Old Trafford.
Supporters who turned out to greet their arrival in Manchester earlier were given short shrift by local police, although, under the circumstances, Terim understands why.
"When we arrived at our hotel, we learned about the two policewomen who died," he said.
"Maybe the reaction when we landed had something to do with that."
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