Tuesday's report said the attack would not focus only on southern Lebanon, as in previous wars.
It said the threat was founded on Hezbollah's perseverance in smuggling weapons into Lebanese territory, evidence of which was discovered by Israel on the arms ship Francop.
Britain's ambassador to Lebanon, Frances Guy, denied having any knowledge of the alleged Israeli threat. "You journalists are always looking for trouble," she reportedly said.
"If it's true, it is unfortunate," she said when pressed, but stressed her disavowal of knowledge.
Earlier Tuesday IDF Chief of Staff Gabi Ashkenazi warned that Hezbollah is currently armed with thousands of missiles, some of which could reach the southern city of Dimona.
"Some of them have a range of 300 km and some of them have a range of up to 325 km," Ashkenazi said, adding that the missiles were ready for use.
"There is a paradox – one hand there is calm, but when you peek over the fence you can see armament and empowerment. If Hezbollah carries out a retaliatory attack for (Imad) Mugniyah it will force Israel to respond and this will lead to deterioration," he said.