Application for an - American Citizen living in Berlin

I will be traveling to Shenzhen in around August 16th for approx. 3 weeks, and I have an appointment to renew my German Visa on August 5th, with hopes of getting a permanent residency. Is it possible for me to apply for my tourist L before my appointment for my German one or do I need to wait until I have renewed my German one? I'm worried I will not have time between my current appointment and the date I'm supposed to fly to Shenzhen. My current German one expires the end of August. Thank you!