However, the 1992 European champions could also qualify from Group I with a win at the Estadio Municipal.
In the wake of the Seleccao's 1-0 friendly defeat against France last month, coach Fernando Santos boldly claimed that his team would be in better shape than Les Bleus by the start of next year's tournament.
Portugal's task is simple. A win or a draw against the Danes will secure qualification. However, defeat could play into the hands of both Denmark and Albania, who are still capable of reaching the finals.
The 2004 runners-up have been in good form since losing to the Albanians in their opening group fixture, winning six consecutive games to move three points clear of the chasing pack.
Not surprisingly, Portugal's biggest threat is likely to come from Real Madrid forward Cristiano Ronaldo, who has scored 26 times in European Championship matches, including five in this campaign.
Ronaldo has been regarded among the best players in the world for a long time, but former international teammate Deco has suggested that his dedicated attempts to be the number one player on the planet borders on a sickness.
However, it was Miguel Veloso who has put Portugal on the brink of the finals after netting a late winner away in Albania last month.
Recent form: LWWWWL
The Danes' long-serving coach Morten Olsen has already announced that he will be retiring after his country's Euro 2016 campaign, but the question will be whether he bows out in France, or not.
A 0-0 draw in Armenia last month left the Scandinavians only a point ahead of Albania and, if they fail to beat Portugal, the Red and White may be facing the prospect of a two-legged playoff.
However, the visitors can take confidence from their defensive record, having conceded only four goals in seven internationals. Only Albania have conceded fewer.
If they are to maintain that record, a lot may depend on the performance of captain Daniel Agger, who has continued to feature prominent in the national team since returning to Brondby.
Like Portugal they have also scored eight times in qualifying, with ex-Arsenal front man Nicklas Bendtner currently Denmark's top scorer with two goals.
Recent form: LWDLWL
The hosts will have Atletico Madrid midfielder Tiago available again after a one-match suspension forced him to sit out the trip to Albania.
Ronaldo is expected to start in Braga, as is former Manchester United teammate Nani, who is one yellow card away from a ban.
Meanwhile, Olsen could recall Christian Eriksen after the Tottenham Hotspur forward missed their goalless draw in Armenia.
Kjaer, William Kvist and Lars Jacobsen are also in contention to start for the visitors, but all three are in danger of picking up a one-game ban, which would keep them out of the playoff first leg, if required.
Portugal possible starting lineup:
Patricio, Vieirinha, Pepe, Carvalho, Eliseu, Pereira, Veloso, Silva, Danny, Nani, Ronaldo
Denmark possible starting lineup:
Schmeichel, Kjaer, Agger, Durmisi, Jacobsen, Krohn-Dehli, J Poulsen, Eriksen, Bendtner, Jorgensen, Y Poulsen
Head To Head
While Denmark need to beat Portugal in order to boost their bid for automatic qualification, their recent record against the Seleccao is far from encouraging.
Of the 15 meetings between the teams, the Danes have won only three and lost 10, including a defeat at Euro 2012.
In the reverse fixture last October, both sides were heading for a draw in Copenhagen before Ronaldo popped up in the fifth minute of stoppage time to snatch three points for the visitors.
We say: Portugal 1-0 Denmark
With Denmark playing their last game, Olsen's side have plenty to play for in Braga. However, Portugal's record against the Scandinavians and their run of form would suggest that Santos's men should secure their place at Euro 2016.