Police believe the man, now in jail for a sex crime, was in the area where the girl, then aged three, was last seen.
Madeleine's parents Gerry and Kate McCann thanked the police, adding: "All we have ever wanted is to find her."
Police are appealing for information about two vehicles owned by the man.
The day after Madeleine vanished, the suspect transferred a Jaguar car to someone else's name.
Madeleine went missing from an apartment on a Portuguese holiday resort on the evening of 3 May 2007, while her parents were with friends at a nearby tapas bar.