The attacks took place between 2004 and 2006.
Madeleine was just three years old when she went missing from her parents’ holiday apartment in Praia Da Luz in May 2007.
British detectives have claimed the man they are hunting for appeared to have “have a very very, unhealthy interest" in white, young girls”.
The attacks, which are being investigated by British police officers, reportedly involved a dark haired man, who entered holiday accommodation, mainly occupied by British families.
The man is described as unshaven, with unkept hair, and is said to have spoken in English with a foreign accent.
Two of the families involved have claimed the intruder wore a distinctive, long sleeved top – with one family reporting the top was burgundy with a white circle on the back.
Detective Chief Inspector Andy Redwood has asked anyone, who may have information, to speak out, saying:
“If you have been a victim of a similar crime please come forward even if you reported the incident to police in Portugal, or anywhere else, please do not assume we have been made aware of it.
He added: “We need to eliminate this man from our inquiries and ascertain whether these offences are linked to Madeleine's disappearance.”
If you think you have some information relating to this, please call 0800 0961011.
Alternatively, you can contact Crimestoppers, anonymously, on 0800 555 111.