Yes you can, but you have to know a very important think... If you want a successful asylum process in Germany, you have to arrive to Germany without having entered another European Union country before, there is already a Dublin procedure, by which it is determined which country is responsible for your case and it will be The country where you entered the European Union in the first instance, it doesn't matter if you only made a connection at an airport. You must take a flight that arrives directly in Germany and that comes from a country that doesn't belong to the European community.
Remember that asylum can only be requested in Germany you have to arrive first and then request it, advise you before coming and avoid waste money, time and energy. Do it the right way.