It has been suggested that a number of key suspects could be questioned in relation to the three-year-old's disappearance in Praia da Luz in 2007.
British officers, accompanied by their Portuguese counterparts, carried out searches earlier this month of three areas of land near to where Madeleine went missing.
She had been in a holiday apartment as her parents Gerry and Kate, from Rothley in Leicestershire, dined with friends nearby.
On finishing the latest search police said it had been the "first phase of this major investigation which has been agreed with the Portuguese".
Tonight neither the Metropolitan Police nor officers in Portugal would make any official comment on the reports.
It has been suggested that UK officers could sit in on interviews carried out by Portuguese police with up to eight people who will attend the station voluntarily this week.
A statement from Scotland Yard during the searches said there was "still a substantial amount of work yet to be completed in the coming weeks and months".
"This recent work is part of ensuring that all lines of inquiry are progressed in a systematic manner and covers just the one hypothesis that she was killed and buried locally," the statement said.
"This is the same as would be done in the UK for a murder or high-risk missing person inquiry."