The mother of a baby boy abandoned on the doorstep of a Queensland home remains in hospital for medical checks.

Police say she is definitely the mother and their investigation is now closed.

The newborn was found tucked up in a wicker basket found on the doorstep of a family at Logan, south of Brisbane, on Saturday.

The baby, who appears to be of Samoan or Pacific Islander descent, remains in hospital because he is underweight.

The Logan family has reportedly dubbed him Moses, a reference to the biblical prophet who was also found in a basket as a baby.

The family has said it's prepared to raise the child but the decision rests with child safety authorities.