The 31-year-old Chelsea midfielder damaged his calf in Germany's final training session on Friday at their Euro 2008 base in Tenero, Switzerland, and has been receiving treatment for the injury.
"We won't give up hope" that Ballack will be able to lead his squad on the pitch, said team manager Oliver Bierhoff.
Although the team flew to Vienna on Saturday afternoon for Sunday's final at the Ernst Happel Stadium, Ballack stayed behind at the team hotel for treatment and a decision on whether he plays will be taken just before kickoff.
Ballack missed the World Cup final loss to Brazil in 2002 through suspension.
He is doubly keen to make Sunday's trophy match after a series of near misses, not least this season with the Champions League final loss to Manchester United, who also beat Chelsea to the Premiership title.
Six years ago he was in the Bayer Leverkusen side which finished runners-up in the German league, the Champions League and the German Cup. The German media suggested that Germany's chances of winning would be hit hard were he to have to sit out Sunday's action.
"Germany is trembling," wrote Bild internet edition, adding Ballack had been complaining of pain since early Friday.