The winner could progress to the round-of-32 if Belgian side Zulte Waregem, who sit second, lose at Group D winners Rubin Kazan.
Maribor go into the encounter with four points from their first five matches, while Wigan sit a place above with one more point, despite losing their past two in the competition.
Wigan's preparation for the trip to Slovenia has not been ideal, with new manager Uwe Rosler only appointed as Owen Coyle's successor on Saturday and the German is determined to give the tie his full attention.
He said: "I know Sunday (against Bolton) is a massive game and I have to be sensible, especially when you have players coming back from injury.
"But when you lose five games in a row your first priority is to start winning football games. So, we will have a competitive team in Maribor. We owe it to ourselves and to the fans who are travelling down there.
"We have to embrace the competition because you never know when Wigan will play in Europe again. We have to get out of this habit of losing games and we have to change that momentum as soon as possible.
"I have a very talented squad of players, I'm looking to play a 4-3-3; the players are very familiar with the formation from the past, from Roberto (Martinez).
"Every player can show themselves now until the transfer window opens, everyone can impress."
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