Madeleine McCann's family believes the police announcement of a new suspect is "potentially very significant".
A family spokesman added that her parents Kate and Gerry McCann have never given up hope that she will be found alive, but they are "realistic".
Madeleine disappeared from her room on May 3, 2007 during a family vacation in the Algarve, Portugal, while her parents were having dinner with close friends at the Praia da Luz resort.
The British and German police have requested information on Wednesday about a German pedophile convict who is currently serving a prison sentence in his home country for sex crimes.
Clarence Mitchell, a family spokesman, told BBC radio: "Kate and Gerry feel that it is potentially very significant."
He added: "They never gave up hope that she can still be found alive, but they are realistic.
"Whatever the outcome of this particular line of investigation, they need to know what happened to their daughter to find peace and bring those responsible to justice."
Suspicion of 43, who was not identified, is described as white, with short blond hair and about 1.80m tall and with a slender constitution when Madeleine disappeared shortly before her fourth birthday.
Police are also asking for information about the movements of two vehicles linked to the suspect during the period surrounding the girl's disappearance.
Both cars, a Volkswagen caravan van and a Jaguar, are now in the possession of the German police.
German police said the new suspect lives in the Algarve between 1995 and 2007.
They added that he lived in a house near Praia da Luz for several years and stole hotels and vacation apartments, in addition to exchanging drugs.
German police said the man was "on several occasions sentenced to prison terms for sexual abuse of children in the past".
They said they were treating the case as a murder suspect and determined the method used to kill Madeleine.
They do not believe the murder was premeditated and said the man was involved in crimes such as break-ins and robberies.