Madeleine McCann, from Rothley, Leics, was nearly 4-year-old when she went missing from her family’s Portuguese holiday flat in an Algarve resort.
Scotland Yard said officers were working closely with Portuguese police and considering their next steps.
They denied asking Portuguese police to make any arrests.
In a statement, the Metropolitan Police went on to say Madeleine’s parents, Kate and Gerry McCann, were being kept up-to-date with their progress.
Clarence Mitchell, a spokesman for the couple, said: “Kate and Gerry remain very, very pleased with the work that Scotland Yard are doing and have been encouraged by Operation Grange [the case review] from the day it began.
“Beyond that, they simply will not comment on what are police operational matters.”
The Met Police statement also said: “Our investigative review is ongoing and we are encouraged by the progress we are making.
“We are reviewing a significant number of documents and continue to identify potential lines of inquiry.
“We can confirm that as part of this process we have identified a number of persons of interest, but any suggestion that the MPS [Met Police Service] is asking the Portuguese police to make arrests in connection with this inquiry is entirely inaccurate.”
The UK review into Madeleine McCann’s case – known as Operation Grange – began last May after Prime Minister David Cameron responded to a plea from her parents.
Its objective is for a team of UK officers to work with the Portuguese authorities with a view to reopening the case, which has been closed since 2008.
As part of the review, a computer-generated image of how Madeleine McCann might look now was produced.
Detectives are also poring over thousands of pieces of information from the Portuguese investigation, inquiries by the UK law enforcement agencies, and the work of private investigators and agencies.
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