Former Chelsea boss Di Matteo has made a positive start to life in the Bundesliga, winning three of his opening four matches in all competitions.
Schalke's strong form continued on Friday with a 1-0 win over Augsburg, with Kirchhoff playing his first full match for the club since his loan move from Bayern Munich in December 2013.
The 24-year-old suffered a long-term ankle injury shortly after his switch, but now feels positive both in terms of Schalke's prospects and his own fitness.
"We currently have a relatively hectic period with many games," he told the club's official website.
"It will certainly take some time before we can show everything that he wants on the pitch. However, we are currently having good results, winning games and scoring some goals. We are working hard now to refine our offensive game."
Having struggled for game time at Bayern after moving from Mainz prior to the 2013-14 campaign, the Germany Under-21 international also feels hopeful of playing regularly at the Veltins-Arena.
"I feel good and fit. There was a good agreement with the coaching staff and I was given enough time," Kirchoff added.
"I've been training a long time in rehab and was brought back to fitness slowly. For me it was important that I came back slowly and did not have to start right from the beginning.
"I feel good, I am happy that my body has held up and hope that this continues."