Fusun Bas, a hospital spokesman, said Sert's tests are "consistent with the early signs of pregnancy."
Sert received a womb transplant in August 2011, and doctors waited 18 months to ensure there would be no problems with the donated organ. The embryo was created using one of Sert's eggs and sperm from her husband, Mustafa Sert, 35.
The baby would be delivered by Caesarean section and the uterus removed after the birth to prevent further complications.
One in 5,000 women is born without a womb, and if Sert is able to successfully carry her baby to term, the procedure will open the possibility of biological motherhood for thousands of women.
Sert is actually the second recipient of a uterus transplant. A Saudi Arabian woman received the first, but the transplant was rejected and had to be removed after 99 days. Two other women in Sweden received donor uteri from their mothers in 2012.