The two sides haven’t met in a competitive fixture since Leigh’s only season in Super League, back in 2005, when Wigan won 62-6 at home and 30-22 in the reverse fixture.
They go head to head at the DW Stadium on Friday for a place in the fifth round.
Wane said: “They’re just down the road, they’re our arch rivals and they have a lot of history in the club, and so do we.
“They have some good people there; Trevor Barton is a man who I respect greatly, and obviously Paul Rowley the coach is doing a great job.
“We’re not going to underestimate them, we’re going to prepare our team the best we can, like we would a Super League club, and hopefully we can progress to the next round.
“At the end of the day, it’s a knock out, so if we don’t perform and don’t go in with our ‘A’ game then we can get turned over and there’s no way back, so we’ve got to make sure we just concentrate and give Leigh the respect they deserve.”
Last season, Leigh made it through to the quarter-finals, where they were beaten by Leeds.
Wigan have won more Challenge Cups than any other club, winning the famous old trophy a total of 18 times, the last coming in 2011.