British detectives have sought the help of Portuguese officers after analysing the mobile phone records, which showed high levels of traffic between the trio's phones.
It came shortly after the three-year-old disappeared in May 2007 from the holiday apartment in Praia da Luz, Algarve, where she was holidaying with Glasgow-born father Gerry, mother Kate and her siblings.
The significant development came after the UK team of detectives launched a fresh investigation, named Operation Grange, into the McCann case last summer and made an international appeal on television in the UK and abroad.
The phones belonging to the individuals, who are thought to have been operating in the Algarve, were described as "red hot" shortly after she vanished.
The International Letter Of Request has been sent to the Portuguese authorities by the Crown Prosecution Service asking them to interview the people. However, their current whereabouts are not thought to be known.
Officers from the re-investigation team are thought to already be in or planning to travel to Portugal.
It is the second International Letter Of Request to be made and comes amid reports that police are poised to make their first arrests.
A spokesman for Mr and Mrs McCann 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 does not prove they have Madeleine but it will rule them in or out of the investigation and that is important.
"Kate and Gerry do not want to build up their hopes too high, but they realise it could be a significant new lead."
The Crown Prosecution Service and Scotland Yard have confirmed the letter was posted last week, but would not comment further.
A Yard spokesman said: "We can confirm a second International Letter Of Request has been sent to the Portuguese authorities by the Crown Prosecution Service in connection with Operation Grange."
Madeleine disappeared as her parents dined at a nearby restaurant with friends. Theories about who was behind it have ranged from a paedophile gang to burglars.
The fresh investigation came two years into a review of the case and saw renewed appeals on Crimewatch and in Holland and Germany.
After shelving their inquiry in 2008 into Madeleine's disappearance, Portuguese authorities said last October that a review had uncovered enough new information to justify reopening it.
In a Christmas message, Mrs McCann, 45, 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."