Two men have been arrested in connection with the alleged theft of sensitive information relating to the Beckhams' security arrangements.
The Beckhams are expecting a third child
The details were stored on a computer, which was allegedly stolen from a company which used to protect the England footballer's family.
The computer files are said to contain details of David and Victoria Beckham's DNA and fingerprints.
Maps and photographs of their home in Hertfordshire may also be in them.
Personal mobile numbers for the celebrity couple and immediate family are also listed, according to an article in Saturday's Sun newspaper.
It claims the computer was taken from a Leeds-based firm, which used to provide security for the couple and their two young sons.
The computer was recovered and handed over to South Yorkshire Police.
A force spokesman has confirmed that two men have been arrested in connection with allegations of theft and blackmail.
They have been released on bail, pending further inquiries.
The Beckhams recently announced they are expecting their third baby in March.
David Beckham has faced criticism over his form in recent months, with a disappointing Euro 2004 and some questionable performances for England.
He was on the losing side as Real Madrid were trounced 3-0 by Bayer Leverkusen in the Champions League on Wednesday.
But he did score one of his trademark free kicks to secure a 1-0 win over Numancia last weekend.