The decision comes following a £5m two-year review of the case, says the Daily Mail, adding a formal announcement is due in weeks.
The newspaper claims Home Secretary Theresa May has agreed to fund a full-scale inquiry into the little girl’s disappearance.
Madeleine was nearly four when she went missing on May 3, 2007, during a family holiday in Portugal.
While the Home Office has not confirmed the report, a spokesman tells the Huffington Post UK: “The Home Office remains committed to supporting the search for Madeleine McCann and we have always said that we would provide the Metropolitan Police with the resources they need to investigate her disappearance.”
According to the BBC, any investigation by Scotland Yard would need the cooperation of the Portuguese authorities.
Madeleine’s parents Kate and Gerry have praised the British police’s continuing efforts to find their daughter.
And last month Detective Chief Superintendent Hamish Campbell said British detectives had identified a “good number” of potential suspects in their hunt for the missing girl, who would now be 10.
He said: “"The purpose of the review was to look at the case with fresh eyes and there is always real benefit in doing so.
"The review has further identified both investigative and forensic opportunities to support the Portuguese. There is more than a handful of people of interest which could be explored further if only to be eliminated.
"The key things are to investigate the case and our work is happening to support the Portuguese."
Speaking to the Evening Standard, he said Madeleine could still be alive, adding: “You cannot exclude it.”
On Monday a Scotland Yard spokesman told Huffington Post UK: “The MPS investigative review into the disappearance of Madeleine McCann continues to make encouraging progress.
“Detectives remain in regular contact with Kate and Gerry McCann and are working closely with the Portuguese police in an attempt to make further progress.”