Child sex offender Christian B is being investigated over possible links to an attack on an Irish woman near Praia da Luz in 2004, according to the BBC.
Officers say they will pass on any evidence to the German police who are also probing the disappearance of three-year-old Madeleine.
A police source told the broadcaster they have "credible information" that 43-year-old German man Christian B may be linked to the rape three years prior to the child going missing.
No suspect was ever identified in the case and forensic evidence is understood to have been destroyed.
The Guardian reported that detectives in Portugal collected the archived case file on her assault last week, quoting a source in the public prosecutor's office.
Rape cases that took place more than 15 years ago cannot be tried in Portugal.
Christian B, who is currently in prison in Germany, was revealed as the main suspect in the McCann case when German and UK police made a fresh appeal for information in June.
He is believed to have been in the area where Madeleine was last seen while on holiday with her parents and siblings.
The Metropolitan Police, who are working with their German and Portugese counterparts, have said the case remained a "missing persons" investigation in the UK.
However, German prosecutors have said she is "assumed" to be dead.