Hariri's resignation, announced from Riyadh, and its aftermath have put Lebanon at the forefront of regional rivalry between Shi'ite-led Iran and Sunni Saudi Arabia Riyadh in recent days.
He suggested he could even withdraw his resignation, provided the Shi'ite group Hezbollah - allied to Saudi Arabia's regional rival Iran - renounces interference in conflicts across the Middle East.
During his visit, Rai is expected to meet King Salman, his son and heir-apparent, Crown Prince Mohammed bin Salman, and Saad al-Hariri, who has been in Riyadh since resigning as Lebanese prime minister on November 4.
"I have resigned. I am going to Lebanon very soon and I will resign in the constitutional manner", he said.
The head of Lebanon's Maronite Catholic community has arrived in Saudi Arabia in the first public visit by a Lebanese official since prime minister Saad Hariri announced his sudden resignation nine days ago.
She added: "It is essential to avoid importing into Lebanon regional conflicts, regional dynamics, regional tensions, that have to stay out of the country".
Hizbollah chief Hassan Nasrallah said last Friday that Mr Hariri was "detained in Saudi Arabia, he is banned from returning to Lebanon".
Hariri became Lebanons prime minister late past year after a political deal that also brought Hezbollah ally Michel Aoun to office as the countrys president.
"To reach a political solution in Lebanon, all political figures must have complete freedom of movement", he told reporters when asked about Hariri.
Mr Hariri sought to dispel speculation that Saudi Arabia summoned him to Riyadh and broadsided him with a demand to resign because he would not confront Hizbollah - a charge the kingdom has denied. Saudi Arabia, denying that Mr Hariri was being held against his will, accused Lebanon of declaring war against it. Rai, whose trip was in the works before the latest political crisis in his country, will take a message to Saudi Arabia that "Lebanon can not handle conflict", his spokesman said last week. Hezbollah says it was the Saudis who have declared war on Lebanon.
Mr Aoun has been convening high-level meetings with Lebanese politicians and foreign diplomats since Mr Hariri stepped down. "We believe it is essential to avoid importing into Lebanon regional conflicts", she said after hosting a meeting of all 28 European Union foreign ministers in Brussels.
The prime minister has not returned to Lebanon since.