If they win as expected and other results go their way, the Danes could seal automatic qualification for next year's finals; meanwhile, their hosts have yet to either score or pick up a point.
Match preview
Taking one step closer to securing consecutive European Championship finals appearances - having missed two of the previous three - Denmark strode to victory over fellow contenders Kazakhstan on Saturday, when Robert Skov scored shortly before and after the break to give them an unassailable three-goal lead.
A crucial 3-1 win in Copenhagen keeps Kasper Hjulmand's men level on points with Group H leaders Slovenia, and the top two have now opened up a four-point gap to both the Kazakhs and Finland with three games left to play.
As a result, Denmark will qualify this week if they complete the formality of beating San Marino for a second time in the process, should Slovenia also avoid defeat against Northern Ireland and Kazakhstan draw with the Finns.
The Euro 92 winners do not have a potential playoff place to fall back on as things stand, after losing out to group winners Croatia in their most recent UEFA Nations League campaign, but games against Slovenia and Northern Ireland next month offer further chances to get over the line.
Having started out on the road to Germany by beating Finland but then letting Kazakhstan come from two goals down with 20 minutes remaining to lose 3-2 in Astana, Denmark have since rallied and are unbeaten since that capitulation back in March.
Now, they could be as little as 90 minutes away from the Euros, and sealing their spot this week would allow Hjulmand to experiment in the Danes' November fixtures.
One of five Danish wins this year came against San Marino in Copenhagen, as they restricted their visitors to just one shot and 14% possession at Parken Stadion in a 4-0 win.
As ever, that has been a familiar tale for the Sammarinese in 2023, with a series of seven straight defeats leaving the international minnows rock-bottom of Group H and trailing six points behind the nearest nation above them.
Including their loss in Denmark, the tiny microstate suffered successive four-goal defeats in September, and Fabrizio Costantini's side returned to action at the weekend with a 3-0 reverse to second-bottom Northern Ireland.
In all, San Marino have conceded 24 goals without scoring at all, therefore holding the worst record of any team trying to reach Euro 2024; since being admitted to UEFA qualifiers back in 1990, they have lost 82 of 83 games in European Championship qualifying.
Also at the foot of FIFA's world rankings, only recent UEFA Nations League campaigns have seen San Marino compete on a relatively level footing, but when pitched against teams of Denmark's stature they are effectively lambs to the slaughter.
San Marino Euro Champ Qualifying form:
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Denmark Euro Champ Qualifying form:
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Team News
Set to captain Denmark again on Tuesday evening, veteran defender Simon Kjaer will become his country's record caps-holder on a total of 130, having pulled level with Euro 92-winning goalkeeper Peter Schmeichel against Kazakhstan.
As both Anders Dreyer and Andreas Skov Olsen were forced to withdraw from Kasper Hjulmand's original squad through injury - joining Benfica's Alexander Bah on the sidelines - Robert Skov started at the weekend, and a two-goal haul could see the Hoffenheim winger keep his place.
Jonas Wind also scored on Saturday and could join Rasmus Hojlund in the visitors' front line, but due to San Marino's limitations some squad rotation could be employed by Hjulmand, with RB Leipzig striker Yussuf Poulsen and Burnley's Jacob Bruun Larsen coming into contention.
Meanwhile, San Marino should once more turn to captain Matteo Vitaioli to lead their attack, though he has scored only once in 88 previous appearances for his nation. Nicola Nanni, of Italian Serie C club Olbia, provides support.
Earlier this year, Roberto Di Maio became the oldest footballer in Europe to make his international debut, and the 41-year-old ex-Lecce defender - who had to wait a decade to be naturalised as a Sammmarinese citizen - is set to start in the hosts' back five.
San Marino possible starting lineup:
E. Benedettini; D'Addario, Fabbri, Di Maio, Rossi, Franciosi; A. Golinucci, Mularoni, Lazzari; Nanni, Vitaioli
Denmark possible starting lineup:
Schmeichel; Kristensen, Kjaer, Christensen, Maehle; Hojbjerg, Eriksen, Norgaard; Skov, Hojlund, Wind