Ideas for the Harry & Paul show were contained on a laptop that was taken from a car in Notting Hill, west London.
The Mail On Sunday reported that the thieves phoned Enfield demanding £750 for the return of the computer, which he refused to pay.
According to the newspaper, the laptop had been in the Mini Clubman owned by the comedian's wife when it was stolen.
Commenting on the incident, a BBC spokeswoman said: "Filming doesn't start for another six months. There were only early thoughts on the laptop and not actual scripts, so it won't impact on filming for the series."
A Scotland Yard spokeswoman stated: "We can confirm we are investigating an allegation of theft from a motor vehicle. There have been no arrests and enquiries continue."