The Danish side, meanwhile, will aim to end their winless start to the season by picking up a victory on Tuesday that would set up a tie against Portuguese giants Benfica.
Match preview
Despite putting in a solid away performance that would have inspired confidence within the squad, Larnaca may have felt disappointed that they let a one-goal lead slip in the first leg.
The Cypriot side battled hard to give themselves the lead in the 81st minute through Adam Gyurcso, however, their one-goal advantage dissipated within three minutes as Erik Sviatchenko levelled the tie.
Although a 1-0 win would have been the perfect result for a club making their Champions League debut, Larnaca can take encouragement from the first leg where they competed impressively with a Midtylland team who are making their fifth appearance in Europe's elite competition.
Not only did the match in Denmark represent Larnaca's first ever Champions League appearance, but it was also Jose Luis Oltra's first game in charge of the Cypriot side.
The new boss will now be plotting how his team can clinch their first win under his stewardship, which would set up a third-round qualifying tie against Benfica.
While Larnaca are just getting used to their new surroundings in a Champions League environment, Midtjylland are involved in the competition for the third consecutive season.
In the previous two campaigns, the Danish outfit have made their way through to the third round of qualifying, but to continue that trend they must win in Cyprus on Tuesday.
Unlike Larnaca - whose domestic season does not get underway until the end of August - Midtjylland are already two games into their Danish Superliga campaign.
Their season began with a 1-1 draw against Randers before they replicated that result in the Champions League, and while Larnaca have had a week to prepare, Bo Henriksen's side were in action once again on Friday.
A 3-1 defeat to Silkeborg would have done nothing to build confidence in the Midtjylland squad ahead of Tuesday's tie, where they will aim to end a winless away run in the Champions League which stretches to six games.
AEK Larnaca Champions League form:
FC Midtjylland Champions League form:
FC Midtjylland form (all competitions):
Team News
After joining from Osasuna in the summer, Oier was one of three summer signings to make his debut for Larnaca in the first leg, and the Spaniard is expected to retain his place for Tuesday's contest.
Kenan Piric and Rafa Lopes were the other two individuals who made their debuts, with the former starting in goal, while Lopes made a substitute appearance, however, the 30-year-old could be presented with a starting place for the second leg.
Lopes is set to lead the line, while Imad Faraj and last week's goalscorer Gyurcso will provide the width for the hosts.
As for the visitors, they are set to be without the services of Evander, who was forced off in the first leg.
Midtjylland are expected to utilise a back three, which is expected to be made up of Henrik Dalsgaard, Juninho and Sviatchenko.
After scoring his first goal of the season against Silkeborg, Anders Dreyer will be aiming to play a match-winning role in Tuesday's contest.
AEK Larnaca possible starting lineup:
Piric; Christoforou, Tomovic, Milicevic, Garcia; Ledes, Sanjuro; Faraj, Trickovski, Gyurcso; Lopes
FC Midtjylland possible starting lineup:
Olafsson; Dalsgaard, Sviatchenko, Juninho; Andersson, Charles, Onyedika, Paulinho; Isaksen, Chilufya, Dreyer
We say: AEK Larnaca 1-0 FC Midtjylland
Although Midtjylland have the greater Champions League experience, they have failed to win any of their last six matches in the competition, and we think that Larnaca will utilise home advantage to advance to the third-round of qualifying.