Further details about the training have not been released due to operational security reasons, though US Air Force special operations aircraft have been seen landing at the Lebanese Special Operations Forces' academia in Hamat.
There was no immediate comment from the Lebanese army.
He stressed that the Resistance is ready to turn over control of the liberated area to the Lebanese Army as soon as it announces its readiness to assume control over them, adding that the liberation of Ras Baalbek and al-Qa'a will be carried out by the Lebanese Army.
The source said the Lebanese army had the military capability to confront and defeat the group without any regional or global support.
Nasrallah's speech comes days after a joint Syrian-Hezbollah offensive culminated in a negotiated deal.
Syria has been locked in a vicious civil war since early 2011, when the Bashar al-Assad regime cracked down on pro-democracy protests with unexpected ferocity.
Beirut- The final preparations for the upcoming Lebanese Army battle against ISIS at the eastern borders with Syria have already been triggered after the completion of a swap deal between Nusra Front and "Hezbollah" and the deportation of Nusra militants from Jurud Arsal to Idlib.
In 2014, the Islamic State and Al Qaeda-linked militants briefly occupied Arsal before the Army joined forces with the militant group Hezbollah to drive them back out of the town.
The Lebanese army did not take part in the fighting between Hezbollah and the former al-Qaeda affiliate now known as Fateh al-Sham Front, but it reportedly coordinated with Hezbollah.
Thousands of refugees travelled to rebel-held northwest Syria alongside the Nusra fighters who left the border area after Hezbollah's assault.
Declaring victory Friday night, Hezbollah leader Hassan Nasrallah said the army was perfectly capable of winning that fight but offered his support should it be needed.
It is this complex relationship between Lebanese governments and Hezbollah that foreigners often find so baffling.