However, the Portuguese police would not be prepared to move, with a source close to the Police Judiciaria labelling re-test ” a total waste of time “.
The evidence was found on the small bed inside the apartment 5A of the Ocean Club by forensic teams after she disappeared in 2007.
Scientists in the Portuguese city of Coimbra were unable to extract a full DNA profile of the sample and its origins remain a mystery.
Now the German authorities want to carry out their own tests on the “potential vital evidence” in the hope that a profile can be found.
If successful, forensic experts would then attempt to match it with the DNA of the German suspect Christian Brueckner, 43.
Portuguese media reports, the Germans have asked for all the evidence provided to them.
Prosecutors in Lisbon, already turned down a Scotland Yard request for a re-test of samples in 2012 and could refuse the German authorities too.
More than 600 samples of hair and saliva were collected in the McCann’s ground floor apartment in Praia da Luz, in 2007.
They remain under lock and key in Coimbra lab, but we do not know if Bruckner of the DNA was checked with the totality of the evidence.
A sample of saliva, found on Madeleine’s bedspread has been rejected because it belonged to a boy who has already stayed in the apartment.
Sources say that this is a second sample of saliva, which were allegedly found on the young pillow, that the German authorities want to test.
They hope scientific advances in the 13 years since it was collected in Portugal could result in a DNA profile obtained.
Former detective of Scotland Yard Peter Bleksley said: “the science of DNA has moved on a long way since 13 years ago, when Madeleine first disappeared.
“There is a lot more complex tests that can be applied now may not be done back in the day.”
But the German request to conduct fresh DNA tests, has triggered a row with the Portuguese authorities.
The Policia Judiciaria source said: “It is a total waste of time.
“What is even worse is that now they want to do in their laboratories, as if ours aren’t good enough.
“Why do they think that their DNA testing centre is better than ours? It is the arrogance of them.”
Mr Bleksley said the dispute “goes down in a very undignified bun fight”.
“They only had a single and overriding goal and that is to get to the truth,” he added.
“There should not be any type of credit research or any kind of muscle flexing whatsoever.
“The law enforcement institutions of different countries seem to be picking fights with the other.”
Last week, a former head of the Portugal National Institute of Legal Medicine, has stated that the samples could still prove vital.
Duarte Nuno Vieira told Portuguese media: “They are always kept in optimal conditions.
“Despite the fact that 13 years have passed, it is still possible today to repeat the tests.
“Things do not happen as fast as they do on TV series such as CSI and can take days, weeks, or even months.
“But in terms of quality, Portugal has some of the highest quality of forensic work of any country.
“In case Maddie the forensic work carried out was quick and competent.
“The fact that 13 years has passed does not mean that the hundreds of samples taken may not be reviewed.
“There was hair, blood and saliva samples from among the enormous amount of material that has been collected and analyzed.
“The results of everything that has been tested in 2007 are available.
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“If there was a new DNA profile with someone whose DNA had to be compared with one or more of these samples, which could be done.
“The identification of persons responsible for crimes can sometimes take decades. The DNA can be preserved for decades to come.”
Portuguese state prosecutors confirmed last week that they had received four requests for international judicial cooperation relating to the case.
The date of the request, and the country has made, have not been made public.
Portuguese newspaper Correio da Manha, on Wednesday, described the current situation as “a stalemate”.
He said that the research of fields related to the Brueckner in the Algarve will not be held unless the German authorities indicate specific locations.
German prosecutors suspect Brueckner killed Madeleine soon after the removal of his television on the night of 3 May 2007. He has denied the allegations.
The 43-year-old is currently serving a sentence of 15 months in prison in Germany for drug trafficking.