The beautiful baby girl was deserted by her mother in the maternity ward at Phuket's Thalang Hospital on Friday.
The new mother said she was heading for the hospital laundry. But she never came back.
Now four couples would like to take home beautiful Baby X, who weighed into the world at a healthy 2.9 kilos.
One of the couples is an Australian who is married to a Thai woman. They told officials at the hospital their only child died at the age of 18, leaving a deep sadness that Baby X would fill.
Doctors and nurses at the Phuket hospital are mystified as to why the newborn's mother left but would like to hear from her to make sure she is ok.
She may be suffering from post natal depression.
The woman told people at the hospital that she'd had a fight with her husband in Krabi, and caught the bus to Phuket to visit her sister, then went into labor on Phuket.
She told doctors that she had two children already. However, the name she gave to officials on admission appears to be false.
Options for the future of the baby will be investigated if the mother does not reappear but laws governing adoptions will have to be observed.