Yes, it is a possible option that is referred to with the term intrafamilial surrogacy by the American Society for Reproductive Medicine (ASRM). In these cases, the surrogate is thoroughly screened as well. In case the intended mother's eggs cannot be used, they will use donor eggs.
Read the full article on: How to Become a Surrogate Mother – Requirements & Qualifications ( 75).

Andrea Rodrigo
Bachelor's Degree in Biotechnology from the Polytechnic University of Valencia. Master's Degree in Biotechnology of Human Assisted Reproduction from the University of Valencia along with the Valencian Infertility Institute (IVI). Postgraduate course in Medical Genetics.