Allawi told the Reuters news agency in an interview on Monday that he had the information from Iraqi and regional contacts knowledgeable about Iraq that "the discussion has started now."

"There are discussions and dialogue between messengers representing [IS leader Abu Bakr] Baghdadi and representing [the head of al Qaeda, Ayman] al Zawahiri," he said.

It is unclear how the two groups would work together, Allawi said.

IS had become an offshoot of al Qaeda in Iraq by 2004, but IS later broke off from the group and became its rival.

The two extremist organizations have divides along ideological, tactical and generational lines - including between older veterans of al Qaeda and a more radical younger generation attracted to IS.

IS on the defensive

The Iraqi military said recently that IS has lost more than three-fourths of the territory it seized when it swept across the country in the summer of 2014.

Iraqi forces with the backing of the US-led coalition - which has thousands of military personnel deployed in Iraq and carries out daily air strikes - began a major offensive to retake Mosul in October 2016.

Brig Gen Yahya Rasool, a military spokesman, told the news agency AP that the group controls less than 30,000 square kilometres in Iraq, or 6.8 percent of the country's territory, down from more than 40 percent at its height.

The full recapture of Mosul, the de facto capital of IS in Iraq, would be a blow to the jihadists' ambition of a cross-border state.

But Allawi warned that retaking Mosul will not be the end of the fight against IS in the country.

"I can't see ISIS disappearing into thin air," Allawi said, referring to the group by a commonly used acronym. "They will remain covertly in sleeping cells, spreading their venom all over the world."