Former Labour leader Ed Miliband, former front-bencher Yvette Cooper, Shadow Foreign Secretary Hilary Benn and Labour's chief whip Rosie Winterton are all invited to attend the midday briefing.
Labour's Shadow Cabinet will then resume their second meeting to discuss whether the party will allow a free vote on military action, or whether Labour leader Jeremy Corbyn will use his power to issue a three line whip to ask them to vote against.
Mr Corbyn said on Thursday that he would not support action but his Shadow Cabinet is divided with Leeds Central MP Hilary Benn clearly in favour. Normanton, Castleford and Pontefract MP Yvette Cooper is among those attending the Privy Council briefing which began at 12 noon.
A draft motion has also been drawn up by the Government, which is based on David Cameron's four 'pillars' of a strategy to defeat Isil involving counter extremism, diplomacy, military action and humanitarian support.
A Prime Minister's spokesperson said this morning that there was still no 'time-table' for a vote this week on strikes however Wednesday and Friday are the only days when one could be tabled due to other Government business.
The invitation to Privy Counsellors comes just days after Ms Cooper wrote a letter to David Cameron to say she was very concerned that so few MPs had been given detailed briefings on such a serious issue, and that the Privy Counsellors needed an urgent meeting on Monday.
Privy Counsellors get far more detailed information than regular MPs on national security, terror threats and military strategy and this information could feed into the Shadow Cabinet's decision.
Ms Cooper, who is now chair of Labour's Refugee Task Force wrote in her letter how she was also concerned about the briefing level for backbench MPs.
She said: "I am concerned that very few Members of Parliament have been given detailed briefing by the Foreign Office and Ministry of Defence on this, and even fewer have had access to full security briefings.
"That makes it very difficult for MPs to contribute to the Government's consideration of what form any motion should take, as well as to respond to the motion.
"For example despite several inquiries I have been advised that the only briefing on offer is a general one from the MoD next Wednesday.
"I'm sure you would agree that this is insufficient - especially as there are suggestions that the Government is considering holding the vote on Wednesday."