Detectives from both countries are running their own investigations and a team from Scotland Yard made the request during meetings with Policia Judiciaria after flying to Portugal this week.
Police are keen to investigate the trio, who are thought to have been working at the Ocean Club complex in Praia da Luz where Kate and Glasgow-born Gerry McCann were staying with their family and friends in 2007.
Officers reportedly believe they were behind a spate of burglaries in the weeks before three-year-old Madeleine disappeared.
Nelson Rodrigues, a barman at the Ocean Club at the time, said a wide range of staff would have had access to rooms.
He said: "There were quite a few staff who had access to keys. Reception staff, the cleaners, and the maintenance men could all get into rooms. Waiters and barmen did not have access to keys. I remember at the time things belonging to guests went missing now and then. Mobile phones, cash, anything valuable lying around."
Police from both countries met in Faro after Scotland Yard sent an international letter of request linked to its own inquiry.
The Met said it had not yet made any arrests and that officers had visited Portugal a number of times in the past 18 months.
British detectives launched a fresh investigation into the youngster's disappearance last July and made renewed appeals on television.