Former Det Insp Dave Edgar said he believes Maddie is still alive, possibly hidden in plain sight on Portugal’s Algarve with no memory of her real identity.
Speaking to the Sunday Express, Edgar said: “There is every possibility that Madeleine is still alive and could be being hidden somewhere.
“When you get up beyond the main strip of the Algarve there’s countless isolated properties where Madeleine could be being held.
“Obviously we had a number of lines of inquiry and some of those lines did lead us to properties which we followed up and handed over to the authorities.”
Edgar, 60, pursued the case as a private investigator upon retirement and was hired by parents Kate and Gerry McCann to probe Maddie’s disappearance for three years.
He reiterated his belief that persons unknown have carried the burden of secrets about the case for a decade. He said any potential witnesses can be confident they will be treated with care and diligence by investigating officers.
It was revealed last month that Metropolitan Police’s Operation Grange probe had been given additional resources to continue its work on the case.
Madeleine was nearly four when she vanished in 2007 from her family’s holiday apartment in Praia da Luz as her parents dined with friends at a tapas bar nearby.
The McCanns have spoken of their bitter regret about leaving her and two-year-old twins Sean and Amelie alone.
The missing girl would now be a teenager and the family have never given up the search and remain hopeful she is alive.