Baby Sunday Rose may not appear in any magazine spreads, as her parents Nicole Kidman and Keith Urban are considering whether to keep their newborns identity a secret.

The new mother and her singer husband are undecided whether to release a photograph of the newborn tot, but if they do it will be for free, reports Australian newspaper The Sydney Morning Herald.

A source tells the publication: "They don't think it's appropriate to make deals. They are still deciding how they feel about (it) - if and when they will release a photo at all. But they realise there is enormous interest from the public and they are grateful and appreciative of that.

"Nicole and Keith have been enjoying their first few days at home with their firstborn tot - Nicole is thinking about things like breastfeeding right now."

Kidman gave birth in Nashville, Tennessee last week to Sunday Rose, who weighed six pounds, seven and a half ounces (2.93 kilograms).

The tot is Kidman's first biological child. She adopted 15-year-old Isabella and Connor, 13, during her marriage to Tom Cruise.