It is the second international letter of request to be made and comes amid reports that police are poised to make their first arrests.
It has been reported that British police want to question three burglars who were operating in the Portuguese resort of Praia da Luz where Madeleine disappeared.
A spokesman for Madeleine's parents Kate and Gerry said: "The letter is a significant development.
"It is necessary for British police to request the Portuguese authorities allow them to operate on their turf.
"It means they have the intention of arresting and interviewing X, Y or Z. We don't know who they have their sights on but it's likely it is the burglars.
"Whether the Portuguese will co-operate remains to be seen. It is a very sensitive issue with differences they have had.
"Police want to be given a chance to arrest key suspects. It doesn't prove they have Madeleine but it will rule them in or out of the investigation and that is important.
"Kate and Gerry don't want to build up their hopes too high but they realise it could be a significant new lead."
The Crown Prosecution Service (CPS) and Scotland Yard have not commented on the detail of the latest letter to the Portuguese, apart from confirming it was sent last week.
A Yard spokesman said: "We can confirm that a second International Letter of Request (ILOR) has been sent to the Portuguese authorities by the Crown Prosecution Service, week commencing 6 January, in connection with Operation Grange."
Madeleine, who was then nearly four, disappeared from her family's holiday apartment in Praia da Luz in the Algarve on May 3 2007 as her parents dined at a nearby restaurant with friends.
British detectives launched a fresh investigation into the youngster's disappearance in July last year - two years into a review of the case - and made renewed appeals on television in the UK, the Netherlands and Germany.
After shelving their inquiry into Madeleine's disappearance in 2008, Portuguese authorities said last October that a review had uncovered enough new information to justify reopening it.
In a Christmas message, Mrs McCann said she and her husband were relieved and buoyed by last year's developments, and urged people to "spare a thought and prayer" for families similar to hers.
In her message, Mrs McCann said: "This year seems to have passed particularly quickly - a sign undoubtedly of a very busy year.
"It would still be a comfort if we could slow time just a little.
"Thankfully however there have been some very positive aspects with regards to Madeleine.
"The Metropolitan Police review becoming an investigation and, more recently, the reopening of the case in Portugal.
"We are incredibly relieved and buoyed by these developments and continue to hope for further collaboration in the near future with the possibility of a JIT (Joint Investigation Team) between Portugal and the UK to enhance the search for our dear daughter."