Detectives were questioning three people in Portimao, the nearest large town to Praia da Luz, Portugal's national news agency Lusa reported, citing unnamed police sources.
British broadcaster Sky News said one of the men who was reportedly being questioned lived at the villa with his British mother. The man's father was Portuguese, the report said. The man had worked as a translator with police investigating the disappearance, according to Sky News.
Police began their search of the villa shortly after dawn after obtaining a search warrant, Portuguese public television Radiotelevisao Portuguesa reported.
The villa is about 100 meters from the Ocean Club holiday village where Madeleine McCann was apparently taken from her hotel room May 2.
Lusa cited unidentified police sources saying they were investigating "strong leads."
Madeleine McCann vanished after her parents left her, and her brother and sister, both aged 2, alone while they went to a nearby restaurant within their hotel complex at Praia da Luz, a vacation resort in Portugal's Algarve region. Last week, police called off their ground search.
Earlier Monday, her father said they were considering how best to use expressions of support, including financial help, in the search for their daughter.
"There have been multiple offers of different forms of help, including financial pledges by people wishing to help Madeleine," Gerry McCann, the father, told reporters outside their hotel.
"We have brought in our lawyers to help us decide how best to use these offers of support to help us find Madeleine," he said in comments broadcast on Portuguese television.
British media have said that promised contributions total some $5.1 million, including reported donations from Harry Potter author J.K. Rowling, tycoon Sir Richard Branson and American Idol judge Simon Cowell. Also, celebrities including soccer star David Beckham have made public appeals for help in finding Madeleine.
Gerry McCann said he and his wife, Kate, had taken strength from the "spiritual outpouring" around the world.
Asked how long they would stay in Portugal, Kate McCann said, "I can't even consider going home at the moment, absolutely can't even let it enter my head."