The Dutch newspaper De Telegraaf said Van der Sloot, a suspect in the 2005 disappearance of U.S. teenager Natalee Holloway, himself told it in a telephone call on Saturday that "a test has proved" the pregnancy.
Van der Sloot's attorney Maximo Altez, told The Associated Press that a woman named Leidy Figueroa Uceda "is registered as a conjugal visitor of Joran. She is registered in the visitors books of the Piedras Gordas prison in Lima."
He denied, however, that he had told the newspaper he could confirm the pregnancy.
"I told them I didn't know anything in that respect," he said.
News media in Peru last year identified Figueroa as Van der Sloot's girlfriend, and said they had conceived a son together, but she denied it.
De Telegraaf said Van der Sloot told it that the woman 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.
Recorded messages on Monday indicated that two telephone numbers registered to Figueroa had been cancelled.
Van der Sloot is a self-described liar, having confessed to killing Holloway 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.
Toby Sterling reported from Amsterdam.