Allawi said he got the information on Monday from Iraqi and regional contacts knowledgeable about Iraq.
"The discussion has started now," Allawi said. "There are discussions and dialogue between messengers representing Baghdadi and representing Zawahiri," referring to Islamic State leader Abu Bakr al Baghdadi and Ayman al Zawahiri, the head of al Qaeda.
Islamic State split from al Qaeda in 2014 and the two groups have since waged an acrimonious battle for recruits, funding and the mantle of global jihad. Zawahiri has publicly criticized Islamic State for its brutal methods, which have included beheadings, drownings and immolation.
It is unclear how exactly the two group may work together, Allawi said.
Islamic State blazed across large swathes of northern Iraq in 2014, leaving the Iraqi central government reeling. Baghdadi declared a caliphate over the territory the group controlled from the al-Nuri mosque in Mosul the same year, which also became a point of contention with al Qaeda.
Last October, Iraqi security forces and Shi'ite volunteer fighters, commonly referred to as the Popular Mobilization Units teamed up with an international coalition, including the United States, to drive Islamic State from of Mosul and the areas surrounding the city.
The group has been pushed out of the half of Mosul that lies east of the Tigris River, but Iraqi soldiers and their allies are now bogged down in tough fighting in the narrow streets of in the Old City of Mosul, west of the river, according to Iraqi security officials.
Islamic State has used suicide bombers, snipers and armed drones to defend the territory under their control. The group has also repeatedly targeted civilians or used them as human shields during the fighting, according to Iraqi and American security officials.
The militant group has lost ground in Mosul but still controls the towns of Qaim, Hawija and Tal Afar in Iraq as well as Raqqa, their de facto capital in Syria.
Even if Islamic State loses its territory in Iraq, Allawi said, it will not simply go away.
"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."