A Syrian source familiar with the matter said the visit was expected to take place within the next two weeks.
Zelenskiy on Monday painted his meeting last week with President Donald Trump as a success that yielded progress on acquiring new air defence systems.
Saudi Arabia reaffirmed its commitment to regional peace, expressing hope that the truce would help de-escalate tensions along the shared border.
After his speech, Trump met with U.N. Secretary-General Guterres for the first time since returning to office in January.