Bayern, who travel to face St. Pauli on Saturday, have a nine-point lead in the league with six matches to go, and hold a 2-1 advantage over Real in their quarter-final after stunning the Spaniards at the Santiago Bernabeu on Tuesday.
"Short answer is no," Kompany, who turned 40 on Friday, told a press conference when asked about birthday celebrations.
"We can only wish for the three points (against St Pauli). I always celebrated birthdays at the stage of semi-finals and quarter-finals so it's a bonus if you get the wins at these moments.
"I am trying to run away from all the birthday stuff," he said. "We are in priority mode. At this moment there are enough emotions in the coming days. Maybe some red wine tonight but first prepare for the match."
Bayern are still in the running for three titles, with a German Cup semi-final against Bayer Leverkusen scheduled for April 22.
They can also set the record for most league goals in a season on Saturday having scored 100 so far, one short of equalling the all-time mark.
Kompany hinted at changes to his lineup for St Pauli.
"I want to have a team that can bring the same intensity and concentration as in Madrid. Normally it is not a problem for us, but at the moment I will not only look at the quality but also how fresh everyone is," he said.
"Whatever changes we make, if we make any, we don't want to lose what we have."
As for the return leg on Wednesday against Real, Kompany said only a win would do.
"A win in Bernabeu and next week we want to win at home. My thoughts on this are very uncomplicated," he added.