Martin Griffiths will travel to the rebel-held capital of Sanaa on Saturday for talks with Houthi leaders and with the head of a truce monitoring committee, Dutch general Patrick Cammaert, said UN spokesman Farhan Haq.
He will then head to Riyadh to meet with Yemen's President Abedrabbo Mansour Hadi and other officials.
The United Nations is hoping to bring the sides together later this month, possibly in Kuwait, to follow up on the progress made in talks in Stockholm in December, diplomats said.
Under the agreement reached in Sweden, the rebels agreed to redeploy from Hodeida, the Red Sea port that is the entry point for food aid to millions of Yemenis on the brink of famine.
"The cessation of hostilities in Hodeida continues to hold," said Haq.
Yemen's government has written to the Security Council to accuse rebels of failing to comply with the ceasefire while the rebels have accused the Saudi-led coalition of carrying out low-altitude flights over the city.
The council is expected to hear a report from Griffiths next week, but no firm date has been decided for that meeting.
The war between the Houthis and troops loyal to Hadi escalated in March 2015, when Hadi fled into Saudi exile and the Saudi-led coalition intervened.
The conflict has unleashed in Yemen what the United Nations has described as the world's worst humanitarian crisis.
Follow us on Twitter: @The_NewArab