By STEPHANIE LINNING FOR MAILONLINE
Scotland Yard announced last year that it would be winding down the search for Madeleine, who vanished while on a family holiday in Portugal nine years ago.
But Theresa May, who has been a longtime supporter of parents Kate and Gerry McCann, might now step in to grant the police inquiry more time.
A source close to the McCanns told the Daily Mirror: 'Kate and Gerry know the inquiry has to end one day but it is possible more time could be granted by Mrs May and her new Home Secretary Amber Rudd.
'Theresa has met the couple in the past and has been very supportive.'
Madeleine was three years old when she went missing from the holiday apartment at the Ocean Club in Praia da Luz on May 3 2007.
Portuguese police, working in co-operation with Scotland Yard, reopened the investigation in 2013 amid talk of fresh leads but last year the Metropolitan Police announced it had reduced the number of officers it had working on the case from 29 to four.
Last year, the Government also revealed that the investigation, codenamed Operation Grange, had cost more than £10million.
Mr and Mrs McCann spoke on the ninth anniversary of their daughter's disappearance in May this year, saying that there is 'always hope' of finding Madeleine.
Kate and Gerry McCann Prime Minister Theresa May
Backing: Prime Minister Theresa May, pictured right today, who has been a longtime supporter of parents Kate and Gerry McCann, pictured left in 2014, might now step in to grant the police inquiry more time
Hope of finding what happened to Madeleine have dwindled in the last year but the McCanns thanked their supporters for keeping her 'in your heart'.
Writing on their official website, Find Madeleine, the couple said: 'As yet another anniversary comes around, we'd like to thank all our supporters for your continued help and commitment in the search for Madeleine, and the hope for her safe return.
'It has been a very long time but the investigation continues, information is still forthcoming and our hope and resolve continue.
'Until we have answers, until there is news (real news!), there will always be hope and we will continue to do everything we can to help find Madeleine.'
On the night of the disappearance, the McCanns had left Madeleine asleep in the apartment while they dined in a tapas restaurant about 100 yards away.
Young Maddie in the last photo taken of her on the day she disappeared in May 2007
An image predicting what Maddie might look like today
A string of public appeals have been made over the last nine years in a bid to help find Maddie (pictured left), including several computer-generated impressions predicting what she would look like now (shown right)
Detectives have explored dozens of theories since she vanished, including allegations she was kidnapped by a paedophile gang, killed during a botched burglary or snatched and sold by child traffickers.
But despite 9,000 potential sightings all over Europe and even further afield the police are no closer to solving the mystery.
Mrs McCann said recently: 'Nine years. Time just goes too quickly. It's the quiet times that are tough. Times when you are thinking about her — or something related to her.
Madeleine was three years old when she went missing from the holiday apartment at the Ocean Club in Praia da Luz, pictured, on May 3 2007. Despite 9,000 potential sightings all over Europe she has not been found
'The urge to look for Madeleine absolutely hasn't changed at all. You hear all the time about people who have been missing for years being found. There have been so many cases like that.
'We will never give up. You couldn't settle if you thought about giving up. I want an end, an answer. Whatever that it is.'
A Scotland Yard spokesman said today: 'The Operation Grange team have considered the recent media speculation but we are not prepared to discuss our ongoing investigation to discover what happened to Madeleine McCann.'
Met Police chief on progress of Madeleine McCann investigation