Whether or not the child is looked after at the moment, you might want to apply for a legal order for the child. You might want to do this if the child is going to stay with you a long time. A legal order such as a Special Guardianship Orderor a Residence Order would give you parental responsibility. That would mean you had the legal right to raise the child, and make some important decisions about the child. You could apply for one of these legal orders before the child comes to stay with you, or after the child has been living with you for a while. For more information about these orders look here.
If the parents make the arrangement directly with you (without social workers being involved), then this will almost certainly be a private arrangement so the child will not be looked after. But it is also important to note that if you are not a close relative (step-parent, grandparent, aunt, uncle or older sibling whether full or half) you need to tell Children’s Services as soon as possible if the child will be with you for more than 28 days. They will check on the arrangement to ensure the child is safe and well cared for. (Confusingly this type of private arrangement is called ‘private fostering’).