The Daily Mirror says Kate and Gerry are hopeful of a possible breakthrough in the six-year case as the team from Scotland Yard discussed developments with counterparts in the Algarve.
A source close to the couple told the Mirror: "Clearly the fact that the police are out there is significant. Kate and Gerry will now be on tenterhooks as they wait for any potential developments.
"The Met are being very pro-active and this is good news in the search for Madeleine and her abductor."
Hopes were raised that a breakthrough was imminent after British police sent an International Letter of Request to authorities in the country asking for help to trace three burglary suspects spotted in the area where Madeleine vanished almost seven years ago.
A source told the newspaper: "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."
The team, headed by Detective Chief Inspector Andy Redwood, who is leading the Met's investigation, met members of Portugal's Policia Judiciaria and prosecutors to request help and discuss leads identified by teams in the UK.
They are seeking assistance to interview the three potential suspects, though Scotland Yard refused to confirm whether a team was in the country or the purpose behind the travel.
The development follows scrutiny of mobile phone records that revealed the suspects repeatedly called each other in the hours after three-year-old Madeleine disappeared from a holiday apartment in Praia da Luz in May 2007.
Metropolitan Police have so far not commented.