A woman who volunteered to carry a cloned child is said to be eight weeks pregnant.
The controversial scientist behind the project made the announcement at a conference in the United Arab Emirates. If it is confirmed this would be the first time a human cloning pregnancy has gone ahead.
Dr Severino Antinori, one of the two specialists leading the programme, told the conference: "One woman among thousands of infertile couples in the programme is eight weeks pregnant."
New Scientistreports he has refused to give further details, such as the woman's nationality, and his office in Rome has refused to confirm or deny the report.
The Andrology Institute of America in Lexington, Kentucky, had originally planned to clone a baby by Christmas last year.
Many countries have banned reproductive cloning and most scientists agree the risks of severe birth defects in cloned children are too high to justify the method.
PA