They already are involved:
Intelligence officers at GCHQ are believed to have made a breakthrough in the search for Madeleine McCann.
Staff at the Doughnut are said to have been helping in the hunt for the missing four-year-old.
According to press reports, staff at the Cheltenham base, using controversial phone-tapping system Echelon, picked up repeated references to a German man and a "little blonde girl".
The mobile phone conversations are believed to be "extremely significant".
The hunt for missing Maddie switched to Morocco on Sunday, with police now reported to be searching for the mystery German.
The calls, all in Arabic and made on a Spanish-pay-as-you-go phone, are said to refer to "the little blonde girl" and Kate and Gerry McCann's meeting with the Pope.
There were repeated references to Morocco, Holland and Germany.
The Arab speakers also talked about ferry crossings from the Spanish port of Tarifa, which could be a crucial lead.
Eight crossings a day are made from Tarifa to Tangiers in Morocco.
Tarifa is just three hours' drive from Praia da Luz, the Port-uguese resort where Madel-eine was snat-ched a month ago.
GCHQ staff are believed to have deployed the Echelon spy system, which listens for and monitors key words and phr-ases in phone conversations.
A source close to the investigation is reported to have said: "The information gleaned from these mobile phone calls is being treated very seriously. It could be extremely significant."
Portuguese police confirmed they are making inquiries in Morocco.
British forensic experts have gone to Portugal to help track mobile phone calls in the Praia da Luz area at the time of Madeleine's disappearance.
Mobile signals can be used to pinpoint exactly where the callers have been.
A spokesman from GCHQ declined to comment. He said: "We never comment on intelligence-related matters. We cannot confirm or deny it."