Celtic's sixth European fixture of the season also will be their first at Parkhead, after they had to use Murrayfield for "home" games against KR Reykjavik and Legia Warsaw because of the Commonwealth Games.
There is a belief around the club that a large, noisy crowd at Parkhead may unsettle Maribor but Mulgrew admitted there was still work to be done after last week's 1-1 draw in Slovenia.
"Everyone knows where we are and the crowd will get behind us," said the captain, who wears the armband while Scott Brown is out with a hamstring injury.
"The fans are much tighter to the pitch at Parkhead than they were at Murrayfield so that makes the atmosphere much better. We're at home so it's up to us to be on the front foot and win the game, but it will be difficult. They're a good team and, while we've got to go forward, we need to be a bit cautious at the same time.
"Attacking the opposition is the way we play at Celtic Park and that's what the fans will expect from us but we'll also be well set at the back. I don't know whether or not we'll need to score but we'll be looking to. We'll see how the game goes and how it pans out.
"We did have a few chances against them over there and maybe we could have taken a few more of them. But at the end of the day a draw was a decent result. Hopefully we'll take our chances this time out. Maribor need to score so they might open up a wee bit more.
"It's hard to say what they'll do. Obviously, they need to score if they're going to go through but they may be patient and try to hit us on the counter-attack. Ideally we'll score a couple of goals.
"They were all right in the first leg. They sat off us in the first half and then pressed a bit more after the break. They have some good, dangerous players."
A year ago Celtic came perilously close to an exit in the Champions League play-off round after losing 2-0 away to Shakhter Karagandy in Kazakhstan before a dramatic 3-0 win in the return leg on a rousing night in Glasgow. "That was one of the highlights of last season," said Mulgrew. "To qualify for the Champions League and to do it the way we did, after having been 2-0 down, was massive. I wouldn't say that you can play without pressure after you've reached the group stage but that's where we want to be and that's our aim every year, right from the start of pre-season training.
"That's our ambition and to achieve it without having had our captain would be something, when you think of what a big player Broony has been for us. We're just looking to get there but there's still a lot to do and we need to be ready for this and approach it in the right way. [Brown] should be back in time for the later games so he'll be cheering us on and hoping we can get there."