Cologne to stick with Schaefer
Schaefer was the club's youth coach before taking over from the sacked Zvonimir Soldo last week.
"At the moment there is no reason to discuss the coach issue," Cologne manager Michael Meier told reporters.
"There is no doubt that both will stay on because it would be silly of us to start talking to other coaches now," he said in reference to Schaefer and assistant coach Dirk Lottner.
The win, their second under Schaefer after their 3-0 win over 1860 Munich in the German Cup in midweek, lifted Cologne to 15th spot on eight points from 10 games.