Scotland Yard boss, Bernard Hogan-Howe, said investigators would be following one remaining line of inquiry, unless any new evidence emerged.
Madeleine vanished at the age of three, while on holiday with her parents in Portugal, in 2007, and, despite a high-profile hunt, no trace has ever been found of her.
Speaking on LBC, Hogan-Howe said: “There’s been a lot of investigation time spent on this terrible case.
“It’s a child who went missing. Everybody wants to know if she is alive and, if she is, where is she, and, sadly, if she’s dead then we need to give some comfort to the family.
“It’s needed us to carry out an investigation, together with the Portuguese, and other countries have been involved. There is a line of inquiry that remains to be concluded and it’s expected that, in the coming months, that will happen.”
The Home Office has granted £95,000 to keep the investigation — which now only has a handful of officers working on it — going for another few months.
Hogan-Howe said: “The size of the team has come down radically. We are now down to two or three people in that team. At one stage, there were about 30 officers in it.
“There is a line of inquiry that everybody agrees is worthwhile pursuing.”
When asked when the probe, called Operation Grange, would end, the Met chief added: “At the moment, it would be at the conclusion of this line of inquiry, unless something else comes up.
“If somebody comes forward and gives us good evidence, we will follow it. We always say that a missing child inquiry is never closed.
“First of all, the line of inquiry that is being pursued, that, obviously, is important and it is important that is resolved, and I think it will be.
“If something new comes forward, we will investigate it, but that line of inquiry, probably at the moment, is the conclusion of this inquiry.”
Hopes were high when the UK investigation into the little girl’s disappearance was launched, in 2011, with Scotland Yard detectives later highlighting a sex offender who had targeted British families with young children who were staying in villas in the same area where Madeleine was last seen.
Despite no obvious progress since then, Detective Chief Superintendent Mick Duthie, who is head of the force’s murder squad, last week said he remained optimistic. He said: “There is ongoing work. There is always a possibility that we will find Madeleine and we hope that we will find her alive.”