The Gunners start their European campaign tomorrow night when they take on the Bundesliga side in Germany.
Following on from Saturday's 2-2 draw with Manchester City in the Premier League, Mertesacker is eager for Arsenal to put in a similar display against Dortmund.
"I think we have to give absolutely everything again to get something out of Dortmund," the Germany international told the club's official website.
"They have a good squad, have suffered a few injuries and I think it's good to have them at the start (of the group). We'll try our best and try to deal with the pressure they will put on us."
Arsenal reached the last 16 of last season's Champions League before being knocked out by Bayern Munich.