The tanned, dark-haired man is suspected of breaking in to 12 properties where British families were staying in the Algarve, Portugal between 2004 and 2010.
In the four incidents, girls aged between seven and 10 years of age were sexually assaulted.
The attacks happened between 2004 and 2006, before Madeleine vanished in 2007.
Detective Chief Inspector Andy Redwood said tracing the man, said to have "an unhealthy interest in young white female children", is one of his priority lines of inquiry.
His team currently have 38 people classed as "persons of interest" to the inquiry and are also sifting through details of 530 known sex offenders whose whereabouts they cannot account for.
Of those, 59 are classed as high priority and some of those are British.