It would be the first time North Korean leader Kim Jong-un has hosted a head of state since assuming power in 2011.
He has undertaken a flurry of diplomatic activity recently, meeting China's president in May, and is expected to attend a summit with Donald Trump this month.
Syria, an ally of the North, has made no comment on the reported plan.
The two countries have been accused of co-operating on chemical weapons. But both nations deny the accusations.
No date for the visit was mentioned by the North Korea's KCNA news agency.