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.