The statement comes as Cameron begins a four-day South East Asia tour of talks with leaders covering a variety of topics, including countering Islamic extremism.
"If there is a threat to Britain or to our people on our streets, and we are able to stop it by taking immediate action against that threat, as Prime Minister I will always want to try and take that action. That is the case whether that problem is emanating from Libya, from Syria or anywhere else," The Telegraph quoted Cameron as saying.
According to the UK paper, Cameron's comments are not a specific indication of the country's readiness to launch airstrikes against Islamic State (IS) militants in Libya similar to those in Syria, but are to point out a readiness for immediate action in the event of a "Sousse-style attack threat."
IS activities in Libya came under the spotlight when reports emerged that the gunman who killed 38 foreign tourists, including 30 British citizens, at the Tunisian beach resort of Sousse on June 26, was trained in a Libyan jihadist camp.
On July 8, Tunisia began the construction of a concrete wall along its border with Libya to limit IS movement into its territory.
IS is a religious extremist group notorious for its many human rights atrocities, including kidnapping and murder.