Repsol Honda star Marquez is seeking to maintain a perfect season that has seen him win all eight races so far.
However, a faltering first session around the Sachsenring saw him unseated at Turn Three, and he could only reach sixth place on the timesheets.
He improved to second in FP2, though that was still not enough to usurp NGM Forward Racing's Espargaro, who showed impressive pace, despite the presence of rain late in the session.
Marquez had led the way through most of the session, but Espargaro's efforts on the soft tyres saw him jump ahead late in the day.
Jorge Lorenzo, who missed last year's race after a crash in practice left him with a broken collarbone, came in third quickest and remained safely on the bike.
Marquez's team-mate Dani Pedrosa also missed last year's race due to illness, he was ninth-quickest.
The top 10 were separated by barely over half a second, suggesting tight qualifying sessions and an exciting race are to follow over the weekend.