The Danes finished with 20 points in Group E to secure a playoff spot behind Poland that finished on top with 25 points.
Five of their last 13 meetings have ended in stalemates and (3.40) is on offer for a repeat of this in the clash.
For the Irish, a narrow 1-0 victory in their last group match against Wales ensured their progress to this stage of the qualifiers having gathered 19 points from ten outings.
They have also missed the last three editions of the World Cup and will be looking to return to the global stage next year.
In addition, Martin O'Neill’s charges have an edge over their hosts having triumphed in five of their previous meetings but are the underdogs and are quoted at (5.50) to upset the odds.
Åge Hareide’s side have only lost one of their last ten home games. Punters can thus back them to avoid defeat in this tie at (1.14).
Denmark have only managed two goals in their last two outings while their guests boast of just six goals in their last five duels. With this in mind, few goals will be expected and Nairabet has priced (1.50) for under 2.5 goals while (1.55) is on offer for both sides not to score.