Since your asylum process is not finished yet you will not be send back to your home country during the process. But if it ends with a negative result it might happen that you get deported if you don't get a "Duldung".
Marrying someone with a right of residence (e.g. a German) can result in a residence permit for you. But the chances for this to work out tend to be low because you need to provide lots of papers and evidence that you are not just marrying someone to stay here.
German authorities want to see your passport, a certificate of birth, a registration card and documents that prove that you are not married yet (or that other marriages have been divorced). Furthermore, all documents provided by your home country need to be checked for authenticity by the German embacy in the country where you are from.
The problem is that deportation will only be suspended when your wedding is imminent. That's why it can be a challenge to provide all required documents on time.
Apart from that, authorities will probably check if your marriage is a fictitious marriage (meaning that you only get married in order to get you a residence permit). Therefore they will interview you and your partner and take a look at your room/flat/house to find out if you are actually a couple or not.
So there is lots of things to keep in mind. Still, I don't want to disencourage you and I wish you and your partner all the best! I hope this answer was helpful to you.
I used the following website (German language) as a source and summarized paragraph a) "Heirat, Kinder – Schutz von Ehe und Familie":