The Houthis' visit, expected in the coming days, will raise hopes of a breakthrough in the quagmire conflict that has left hundreds of thousands dead through direct and indirect causes such as famine.
It comes five months after Saudi officials held talks in Sanaa, and as a UN-brokered ceasefire continues to largely hold despite officially lapsing in October.
"There are preparations for a Houthi delegation to visit Riyadh within the next 72 hours," a Yemeni government official familiar with the situation told AFP.
A Western diplomat in Yemen confirmed the visit, saying it may take place within the next two days. Saudi officials did not immediately respond to a request for comment.
Ali al-Qhoom, a member of the Houthis' political council, also announced the visit on X, formerly known as Twitter.
Yemen was plunged into war when the Houthis seized control of the capital Sanaa in September 2014, prompting the Saudi-led intervention the following March.
The ensuing fighting has forced millions from their homes, causing one of the world's worst humanitarian crises in a country already pummelled by decades of conflict and upheaval.
The six-month ceasefire that expired last October is still mostly holding but moves towards peace have been slow since the Saudi delegation visited Sanaa in April.
A delegation from Oman, which plays the role of mediator, arrived in Sanaa on Thursday, Yemeni government officials said -- days after Saudi de facto ruler Crown Prince Mohammed bin Salman met Oman's sultan en route from the G20 summit in India.
Qhoom, from the Huthis' political council, said the rebels' delegation would fly to Saudi Arabia on an Omani plane.
"Optimism exists regarding the mediation and the Omani efforts to achieve peace in Yemen," he posted on X.
'From the back rooms to the living room'
The head of the Sanaa Center for Strategic Studies think-tank, Majed al-Madhaji, told AFP that the Houthi visit "is like moving the relationship between the Houthis and Saudi Arabia from the back rooms to the living room".
By organising talks in Riyadh, both sides are "legitimising this relationship and giving it an additional impetus".
"On the political level, it is an advanced step to end Saudi Arabia's direct role in Yemen and for the Huthis to acknowledge its role as a mediator," in addition to being one of the parties to the conflict.
Moves towards peace in Yemen have accelerated since heavyweight regional rivals Saudi Arabia and Iran announced a surprise rapprochement in March, seven years after they broke off ties.
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