British detectives investigating the disappearance of the youngster in May 2007 are looking at five cases in which young girls were sexually assaulted during holiday home break-ins by a lone intruder in the Algarve.
They were only reported to British police following a public appeal for information in March.
One of the attacks that has now come to light was in 2005 on a 10-year-old girl in Praia da Luz, where Madeleine, then three, vanished two years later.
Investigators from Scotland Yard are poised to stage operations on Portuguese soil and are waiting for an official agreement later this week.
Deputy Assistant Commissioner Martin Hewitt said he was cautiously optimistic officers would be able to act soon.
He said of the report of the sexual assault on a 10-year-old girl: "This offence now takes us into the resort, and of course is very important in investigating Madeleine's disappearance."
Officers are looking at a total of nine sexual assaults and three "near misses" on British girls aged six to 12.
Mr Hewitt said he believed all the assaults involved the same man breaking into holiday villas occupied by British families in the Western Algarve region of Portugal. Five of the assaults came to light following a new appeal about the case.
"There are features within these new crimes that make us absolutely confident that they are part of a series," he said. "We are looking at one offender."
Madeleine disappeared from her room at the Praia da Luz holiday resort in the Algarve in May 2007 while her parents Kate and Gerry, who is originally from Glasgow, were dining with friends at a nearby restaurant.
Last month, police said some of the victims had given a similar description of the attacker as being tanned and unshaven with dark, unkempt hair.
He spoke English with a foreign accent and two of the victims described him as wearing a distinctive burgundy top, with long sleeves and a white circle on the back.
Police in Portugal shelved their inquiry into Madeleine's disappearance in 2008 but British detectives launched a fresh investigation in July last year - two years into a review of the case. Portugal has declined to set up an official joint investigation with the Metropolitan Police.
Scotland Yard made public appeals to try to trace the paedophile last month and so far more than 500 people have made contact with information. Police said it had led them to identify the five sexual assaults and one near miss, including the attack on the 10-year-old girl.
Mr Hewitt said: "In this new tranche of information we have got one crime which is very clearly in the heart of Praia da Luz in 2005, on a young, white, 10-year-old girl.
"Clearly the fact that we've now got an assault that is in the heart of Praia da Luz, very close to where a previous matter had been reported, means that we are even more interested in this as part of the inquiry."
There is a £20,000 reward for information leading to the arrest and prosecution of those responsible for Madeleine's disappearance.
Mr Hewitt said: "I am cautiously optimistic that in the not-too-distant future we are going to start to see activity."
The police officer said Prime Minister David Cameron and Home Secretary Theresa May have expressed a personal interest in the case, and stand ready to intervene to press the Portuguese authorities for help if necessary.