The British racer, 25, who lies only seventh in the championship for the AMG Mercedes team after a trio of sixth places in the opening four races, has fallen down the hierarchy of the team this year.
And he has also been out-classed by former champion Gary Paffett in a year-old machine and rookie Paul di Resta in a 2005-spec Persson-run car.
"Four races and three sixth positions - I am not satisfied. I can do better, and I want to prove it in Nuremberg," said Green.
Two in a row for Tomczyk
Green's record at the street circuit is a poor one though, as he has never even finished there in his two previous starts.
However, should he turn a corner, he could yet become a championship contender as he only trails leader Martin Tomczyk by 12.5 points.
- Jamie O'Leary -
Nurburgring DTM win for Tomczyk
Spengler tops Nurburgring warm-up