Officers believe the woman – thought to be Eastern European – could be the missing link in the search for Maddie.
She reportedly lived near the McCann’s family home in Praia da Luz, Portugal, when the three-year-old disappeared in May 2007.
A source told The Sun: “She may have seen or heard something which to her may seem insignificant but to us could prove vital. If she recognises herself she should contact police."
Scotland Yard’s £12 million hunt for Maddie – Operation Grange – has now been handed another £154,000 as cops try to track the witness.
Maddie's former GP mum Kate, 49, and heart specialist dad Gerry, 48, said they were “incredibly grateful” the police search would continue.