The visitors managed to record a draw against England on matchday two, increasing the pressure on the home side to get maximum points on the board to move off the bottom of Group A2.
However, recording just one point from the fixtures against Belgium and England without scoring a goal has left the recently-appointed head coach with work to do in order to convince supporters that he is the right man for the job.
Regardless of the routine 4-0 victory over the Faroe Islands earlier this week, Hareide needs his players to raise their game in a competitive fixture, especially against the weakest opposition in this group.
The 48-year-old has plenty of time to get his side firing ahead of Euro 2020, but he will be aware that he can ill-afford another negative result at this stage of his tenure.
Denmark have not recorded a win over strong opposition since edging out Switzerland by a 1-0 scoreline in a qualification fixture 12 months ago.
As far as Iceland are concerned, Erik Hamren will want to build on Thursday night's excellent 2-1 victory over Romania in the Euro 2020 playoffs.
After Gylfi Sigurdsson struck twice during the opening 45 minutes, the Scandinavian outfit were able to hold onto their lead to put them within one win of another appearance at a major tournament.
Ideally, Hamren may have wanted the opportunity to rest several members of his limited squad, but facing the Danes on home territory theoretically represents their best chance of getting maximum points on the board in this group.
If Strakarnir okkar suffer defeat in this contest, it would leave them requiring a minimum of four points to have a chance of avoiding relegation to Division B.
Iceland Nations League form: LL
Iceland form (all competitions): WWWLLW
Denmark Nations League form: LD
Denmark form (all competitions): WWDLDW
Despite being used in attack against Romania, Gylfi Sigurdsson could drop back into Iceland's midfield for this fixture.
Christian Eriksen will be one of several players who retain their place in the Denmark side after the comfortable victory against the Faroe Islands.
Iceland possible starting lineup:
Halldorsson; Palsson, Arnason, Ingason, Magnusson; A.Sigurdsson, Bjarnason, G.Sigurdsson, J.Gudmundsson; A.Gudmundsson, Bodvarsson
Denmark possible starting lineup:
Schmeichel; Wass, Kjaer, Christensen, Skov; Delaney, Hojberg; Poulsen, Eriksen, Braithwaite; Dolberg
We say: Iceland 1-2 Denmark
Both nations may be caught between wanting to play offensive football and ensuring that they do not concede at the other end. That should make for a competitive affair, but we feel that the visitors should have enough quality in the final third to edge out the minnows of the group.