British expat Mr Murat, who lives with his mother in a villa less than 100m from the spot where Madeleine was last seen, was taken in for questioning by police 11 days after the four-year-old disappeared in May.
Police searched his house and garden using specialist sniffer dogs after suspicions were aroused over his interest in the case.
Offered police help
Mr Murat, 33, whose father is Portuguese, had earlier offered his services as a translator to police working on the case and became a familiar sight around the crime scene in the days after Madeleine's disappearance.
After questioning the property consultant for several hours at their local headquarters in the town of Portimao, Portugal's Policia Judiciaria (PJ) declared him an "arguido" – or official suspect – in the case.
They imposed restrictions on his movement and took him in for further questioning later.
No formal charges
He has never been formally arrested or charged.
Madeleine went missing from her family's rented holiday apartment in Praia da Luz on the Algarve on the night of May 3 while her parents Gerry and Kate were eating tapas in a restaurant nearby.
The McCanns were themselves declared arguidos after tests on DNA samples found in their hire car were taken as suggesting Madeleine's body had been transported in the vehicle.
They strenuously deny any involvement.
The respected Portuguese weekly newspaper Sol reported that Mr Murat had now been told that police have no case against him.
But he is to remain an arguido until the investigation is complete to avoid compromising other ongoing inquiries, the newspaper says.
Detectives are reported to be investigating the McCanns' movements in the hours immediately leading up to Madeleine's disappearance amid claims that there is a "missing six hours" where Madeleine was not seen by anyone outside their group of friends.
But a source close to the McCanns gave the most detailed account yet of where the family had been on the afternoon of May 3 and insisted there were both written records and witnesses to prove it.