The English side are far better placed to do that than the German champions as they lead the group with eight points, one clear of Olympique Marseille, who in turn are three ahead of Dortmund with Olympiakos Piraeus in last place on three.
A spot in the knockout round for the 12th successive season is assured if Arsenal win and if the other group result goes their way they could qualify with a draw at home, where they have only lost one of their last 36 Champions League matches.
Their record against German sides is also good at home, winning their last five encounters.
Arsene Wenger's side have recovered from a poor start to the season and continued their revival with a fifth successive Premier League win at Norwich City on Saturday to take their recent unbeaten run to eight matches in all competitions.
"Five weeks ago we were 17th in the league and I had to answer a question about whether I thought we would battle relegation," Wenger told reporters.
"At the time I said no but in football things change quickly. We are back in a stronger position."
Arsenal have relied heavily on Robin van Persie this season and he scored both goals at Norwich, taking his tally to 31 in 29 league games this calendar year.
The Dutchman, who also scored Arsenal's goal in their 1-1 draw in Dortmund in September, did not start the drab 0-0 home draw with Marseille three weeks ago when Arsenal squandered the chance to make the last 16 with a victory.
"WEEK OF TRUTH"
Dortmund, who won their first group match at the fourth attempt when they beat Olympiakos 1-0 on November 1, will take great heart from their 1-0 win over Bundesliga leaders Bayern Munich on Saturday - their sixth league win in their last seven matches.
Dortmund grabbed their so-called "week of truth" by the horns, winning 1-0 with a second-half goal from Mario Gotze to close to within two points of the top.
Coach Jurgen Klopp could not have hoped for a better warm-up ahead of their visit to Arsenal, where they have to win to guarantee they stay in contention for a spot in the first knockout round with a final group match to play.
"We are really looking forward to Wednesday. We beat Bayern and we have no real time to celebrate. But we are fit, we are young and we are hungry for success so we want to put in a super performance in London," said midfielder Kevin Grosskreutz.
Defender Patrick Owomoyela, who has been out since October, returned to the Dortmund bench for the Bayern game with defender Marcel Schmelzer also back in action.
Klopp will again be without defender Neven Subotic, who fractured a cheekbone two weeks ago and is not expected to play again this year.
"The win in Munich was great but it also took a lot of energy and we cannot expect the match in London to be any easier," said club chief executive Hans-Joachim Watzke. "But we are on a good run and will go for it."
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