The change in the law is to make claiming maintenance from the biological father easier. The measure, known as the "milkmen's kids law" in local media, is said to pass in the cabinet by Wednesday (31 August) before going to parliament.
Women would be required to keep the father's name anonymous for "serious reasons". Justice Minister Heiko Maas said: "We need to offer more legal protection for 'false' fathers to seek financial compensation".
According to the precise phrasing in the new law, the mother has to name the man "who she slept with during the time of conception".
It would also work in the interest of men falsely named as the father, as they could claim back funds paid out for a child they had erroneously believed to be their natural offspring. Another section of the bill also states that children can take the name of their biological father, once his identity has been revealed.
The ruling in Germany's highest court in March 2015 stated that there was no legitimate reason to make mothers of so-called 'cuckoo children' to name the biological father.
The new law still needs parliamentary approval and to limit the 'false' father's monetary claim to two years' worth of maintenance costs. A judgment by the Federal Constitutional Court of February 2015 added the caveat that providing information on the identity of the father constituted a serious threat to the mother's right to privacy.
How many "cuckoo children" there is unclear, but some studies put the number at 10% for children aged between four and under. A paternity discrepancy study in the British Medical Journal stated that the rate was approximately 4% - so that one in 25 children was fathered by someone other than the man who believes he is the father.