The Russian and English teacher's pregnancy follows several attempts abroad at artificial insemination over the last year and a half, German broadcaster RTL said.
The woman, Annegret Raunigk, decided to try to have another child because her youngest daughter, who is nine, wanted a little brother or sister, RTL said on its website.
The TV channel will broadcast an interview with the expectant mother, who has seven grandchildren, on Monday evening.
It said the pregnancy had so far been without any major complications and that if everything went well, the babies were due in the summer and that Raunigk would be the world's oldest mother of quadruplets.
Mass circulation newspaper Bild am Sonntag also reported the four-baby pregnancy, quoting the mum-to-be as saying the news had initially come as a shock.
"After the doctor discovered there were four, I had to give it some thought to begin with," Bild quoted her as saying, adding however she had not considered it an option to reduce the number of embryos.
Asked about the moral implications, RTL quoted her as saying: "I think, one must decide that for oneself."
Bild also reported on Raunigk 10 years ago when she gave birth to her 13th child and quoted her at the time as saying she had only initially envisaged having one.