The two sides, who will meet for the very first time in a competitive fixture, are two of only three teams who are yet to score in this year's competition.
Rangers missed the chance to extend their lead at the summit of the Scottish Premiership, as they played out a 1-1 draw at home against high-flying Hearts last weekend.
John Lundstram's long-range effort put the Gers in front five minutes before half time; however, the hosts were unable to hold onto their lead as Craig Halkett's 90th-minute header at the far post forced the two sides to share the spoils.
Steven Gerrard's men remain at the top of the table, with a one point lead on their nearest challengers Hearts and four points clear of Glasgow rivals Celtic.
Rangers now turn their attention back to the Europa League, where their form needs to improve if they are to progress to the knockout rounds for the third successive campaign.
The Gers have already suffered 2-0 and 1-0 defeats to Lyon and Sparta Prague respectively and another loss on Thursday would seriously damage their hopes of advancing from Group A.
Rangers have lost three of their last four home games in all European competition, as many defeats as in their previous 26 matches at Ibrox in Europe; however, Gerrard should be confident that his side have the strength to overcome Brondby in midweek.
Brondby's first European campaign since 2008-09 has arguably begun slightly better than expected, as they have managed to claim a point from their opening two group matches.
The Group A outsiders played out a goalless draw at home against Sparta Prague in their opening fixture, before suffering a 3-0 defeat away against one of the tournament favourites Lyon last month.
Since their loss in France, Niels Frederiksen has seen his side pick up four points from their last two Danish Superliga matches, drawing 1-1 against Randers before securing a dramatic 3-2 victory at home against Vejie BK, an encounter which saw Mikael Uhre and Christian Cappis score in the final eight minutes to seal all three points.
Brondby head to Ibrox having played in Scotland on three previous occasions in European competition, winning each of their last two visits against Aberdeen and Hibernian in 1996 and 2016 respectively.
The Boys from Vestegnen, however, have lost 10 of their last 11 away games in Europe and they will need to be on top of their game if they are to claim any points against Rangers.
Rangers will assess Ryan Kent's hamstring injury ahead of kickoff, with Gerrard hopeful that the winger can feature on Thursday.
Midfielder Ryan Jack is slowly being integrated back into first-team training after recovering from a calf injury, but the 29-year-old is not fit enough to feature this week.
As for Brondby, first-choice goalkeeper Mads Hermansen is suffering with an ankle injury and will miss the trip to Ibrox, though Frederiksen has stated that the 21-year-old should not be on the sidelines for too long.
Striker Uhre, who is the club's top goalscorer so far this season with nine strikes in 16 appearances, is expected to start up front alongside Simon Hedlund.
Rangers possible starting lineup:
McGregor; Tavernier, Goldson, Balogun, Barisic; Aribo, Davis, Kamara; Hagi, Morelos, Roofe
Brondby possible starting lineup:
Mikkelsen; Borkeeiet, Maxso, Tshiembe; Bruus, Slimane, Radosevic, Frendrup, Mensah; Hedlund, Uhre
We say: Rangers 2-1 Brondby
Although Rangers have struggled to put a consistent run of form together in recent weeks, Gerrard's side should have enough quality to claim all three points on Thursday.
Brondby should not be taken lightly, however, and could make it a challenging evening for the Gers, especially if they perform as well as they did against Sparta Prague.
body check tags ::
Previews by email