The 41-year-old singer and her husband Rene Angelil, 67, were told by doctors in August she was pregnant after undergoing a course of in vitro fertilisation (IVF) treatment, but days later were told it hadn`t worked.
Despite more subsequent attempts at the treatment, Celine and Rene are refusing to give up hope of having a sibling for eight-year-old son Rene-Charles.
Rene said: "Dr. Zev Rosenwaks believed that the procedure/pregnancy took, but that wasn`t the case. We found out some days later. We were shocked.
"We are living the reality of the majority of couples who have to use IVF. The process can be long and arduous.
"But today, we are full of confidence. Celine is more determined than ever. She doesn`t let go."
The couple - who conceived Rene-Charles after fertility treatment - are now preparing for another course of treatment in New York this weekend.
Rene added to Canada`s Journal de Montreal newspaper: "I admire all the women who go through such a tough process. Since April, she has undergone numerous examinations, multiple hormone injections and blood tests.
"Celine and I didn`t get discouraged - we put our faith in life and in the stars."