The Peruvian newspaper La Republica said the Dutchman, 22, flew into a rage when Flores, 21, opened his laptop and saw material about the 2005 case of the Alabama teen.
Flores was found dead last Wednesday. Van der Sloot reportedly confessed to her murder on Monday.
According to the newspaper, Van der Sloot said in his confession: "I did not want to do it. The girl intruded into my private life. She had no right. I went to her, and I hit her. She was scared. We argued, and she tried to escape. I grabbed her by the neck and hit her."
If true, the reports would focus even more attention on Van der Sloot's possible involvement in Holloway's disappearance five years ago in Aruba. Van der Sloot was arrested and charged twice in the case but released both times.
Van der Sloot appeared to confess to the Holloway crime in 2008 on a secretly recorded video, allegedly telling a friend he had disposed of her body. He later said he had lied on the recording, which had been arranged by a Dutch crime reporter.