Search teams are expected to start excavating a number of sites in Praia da Luz, where Madeleine - then aged three - went missing on May 3 2007, after they were given permission by Portuguese authorities.
But it is believed that a request to search the homes of three men suspected of a number of break-ins before the youngster's disappearance has been turned down.
It is also thought that friction has developed between police teams over the media coverage of the latest developments. Scotland Yard commissioner Sir Bernard Hogan-Howe told Sky News: "There are always going to be complications when you have got one police force in one country working with the police force of another.
"[The police and the media] have both got to be sensitive to these things."
In a statement on their Find Madeleine website, Kate and Gerry McCann said: "There is an ongoing, already challenging, police investigation taking place and media interference in this way not only makes the work of the police more difficult, it can potentially damage and destroy the investigation altogether - and hence the chances of us finding Madeleine and discovering what has happened to her.
"As Madeleine's parents, this just compounds our distress."
The request to excavate several sites in the area is not thought to necessarily be in connection with a search for Madeleine's body or remains and is thought to be among a series of requests made by British detectives in connection with the investigation.