The key piece of evidence -- a torn condom -- given to Swedish police by the alleged victim, was examined at two forensic laboratories but no conclusive evidence of Assange's DNA was found on it, the Daily Mail reported.
However, the same forensic teams have found DNA "thought to belong to" the WikiLeaks chief on another condom submitted by the second alleged victim.
Assange's lawyers have said that the fact no DNA could be found conclusively on an apparently used condom suggests a fake one may have been submitted.
WikiLeaks founder Julian Assange
The revelation is contained in a 100-page police report written after witnesses were interviewed and forensic evidence examined.
The report, seen by Assange's lawyers, has led to Swedish officials requesting his extradition from Britain to stand trial.
The 41-year-old Assange is yet to be charged with any offence.
Assange, who denies allegations of rape and sexual molestation, has been fighting extradition to Sweden for the past two years. He claims it is a ruse to send him to the US where he could face trial for espionage.
He is currently holed up in the Ecuadorian embassy in London after being granted asylum by the country's president, Rafael Correa.
In the report, the first alleged victim claims she was sexually molested by Assange at her flat in Stockholm on several occasions.
She claimed Assange "deliberately ripped a condom" before wearing it so that he could have unprotected sex with her against her will, the Daily Mail said.
The second alleged victim told police she was "raped" by Assange when she was asleep.
But during a police interview, the woman apparently suggested that she did not mind Assange having unprotected sex with her.