Although a draw is enough to qualify for next year's European Championship, Portugal captain Cristiano Ronaldo is out for a win at Denmark on Tuesday.
Both Portugal and Denmark have 16 points in Group H, with the Danes guaranteed at least a playoff spot. If Norway beats Cyprus in another group match and Denmark wins, the Portuguese could mathematically be pushed down to third, but it would need to lose by a big margin or have the Norwegians win by one.
''I think we have the ability to go to Denmark and win and qualify,'' Ronaldo said. ''We know a draw is enough, but we want to win. That's the way we are.''
If Portugal wins the group, the Danes could still earn a direct berth for Euro 2012 as the best runner-up.
Last year, Portugal beat Denmark 3-1.
''We would obviously would like to win the group,'' Denmark striker Nicklas Bendtner said. ''We can do this on Tuesday.''
It was Bendtner who scored both goals in Denmark's 2-0 win over Norway last month that kept the Danes in the hunt for a spot at the tournament in Poland and Ukraine. The striker is expected to lead the Danish attack backed by Dennis Rommedahl and Michael Krohn-Dehli.
But Portugal has played Denmark 11 times, winning seven.
''We have an opportunity, we fully believe in it. We have the quality needed,'' Denmark coach Morten Olsen said.
''We know that we're facing a top class team but we have a good hunch and we have a plan for how it will happen,'' he said.
Olsen earlier said Portugal is ''hungry as a team,'' stressing that the team has five straight wins under coach Paulo Bento, who took over in September 2010.
Portugal reached the Euro 2004 final at home but has never won an international trophy.
On Friday, Nani scored twice as Portugal beat Iceland 5-3, but the Portuguese defense looked shaky. Pepe is injured while Ricardo Carvalho is out because of a one-year suspension.
Iceland and Cyprus have no chance of qualifying.