Cologne travel to the Imtech Arena on Saturday with Hamburg sitting two points off the foot of the table.
Hamburg avoided their first relegation last season, but have been unable to turn their fortunes around in the current campaign.
However, it is not a change in goal that will improve their fortunes, according to Zinnbauer, after only conceding 19 goals in the first half of the season – the fourth lowest in the division.
That means Jaroslav Drobny will continue as first choice, leaving Germany international Rene Adler on the bench as back-up.
"Drobo is playing, he has the edge," Zinnbauer told Bild. "I have already spoken with Rene.
"He will not give up the fight, but the decision was well received."
Hamburg's problems at the other end of the pitch are stark, with just nine goals from 17 league games.
Cologne have the next worst record with 17 goals.
