The Dutch newspaper De Telegraaf cited Van der Sloot's lawyer Maximo Altez as saying the pregnancy is past its third month, and Van der Sloot himself as having confirmed the news in a telephone call on Saturday.
"A test has proved" the pregnancy, the paper quoted Van der Sloot as saying.
The woman, identified by the paper only as "Leidi," was said to have become pregnant during an unsupervised visit with Van der Sloot. It was not clear whether that is allowed or possible under Peruvian prison rules.
Media in Peru last year identified a woman named Leydi Figueroa Uceda as Van der Sloot's girlfriend, and said they had conceived a son together, but she denied it. Altez then described the pair as "friends."
In De Telegraaf Van der Sloot said "Leidi" uses the birth control pill but had apparently forgotten to take it and she would not have an abortion due to her Catholic faith. He said he didn't have DNA proof the child is his, but he believes it to be.
Van der Sloot is a self-described liar, having repeatedly confessed to killing U.S. teenager Natalee Holloway, who disappeared in 2005, and later retracting the confessions. He is the last person known to have seen her alive.
He was convicted for the 2010 robbing and killing of Stephany Flores in a Lima hotel room after meeting her in a nearby casino. He is wanted by authorities in the U.S. for allegedly extorting money from the Holloway family on the promise of revealing the location of her body.
He could resist extradition to the United States, where is wanted in the Holloway case, if he obtains Peruvian nationality. That would be a possibility if he becomes the father of a Peruvian child or if he marries a Peruvian citizen.
Van der Sloot is appealing his conviction.