The 28-year-old is currently serving a 28-year sentence for murdering a young Peruvian woman in 2010. He is also suspected in the 2005 disappearance of Natalee Holloway in Aruba.
In a telephone interview with Dutch newspaper De Telegraaf, Van der Sloot identified the mother as "Leidy" and says she is past her first trimester. He denied, however, that he had told the newspaper he could confirm the pregnancy.
The prison has Leidy Figueroa Uceda listed as Van der Sloot's conjugal visitor, according to attorney Maximo Altez. They reportedly met through another inmate.
Van der Sloot was convicted for the 2010 robbing and killing of Stephany Flores in a Lima hotel room after meeting her in a nearby casino. Van der Sloot is appealing his conviction.
He is also wanted by U.S. authorities for allegedly extorting money from the Holloway family on the promise of revealing the location of her body.
He could resist extradition to America if he obtains Peruvian nationality, which could be made possible if he becomes the father of a Peruvian child or if he marries a Peruvian citizen.
The Associated Press contributed to this report.