Dad duty: Brad Pitt with adopted daughter Zahara in Los Angeles yesterday
The couple already has impressive security at their California home, which includes a ?120,000 state-of-the art control room manned by at least four staff.
Motion tracking cameras with ultra-sensitive detectors alert security to any possible intruders.
Observers say their security bill for 2008 could top ?2.5million.
As well as Shiloh, they have three other children, Maddox, six, Pax, four, and Zahara, three.
On 2 February, at the Santa Barbara Film Festival, she said: "I like being a mum. That's my big passion."
A spokeswoman for the couple did not return calls today, but Brad Pitt has reportedly denied Shiloh has been targeted.