Yes. A child born in Germany (on or after 1 January 2000) can acquire German nationality, even if neither of the parents is German. The only precondition is that one of the parents has been legally and habitually resident in Germany for eight years and has a permanent right of residence. The child must however decide at some stage between the age of 18 and 23 whether to retain his/her German nationality or another nationality acquired by birth.
For further advice, please contact the competent authorities at your place of residence.