Displaced Yemenis receive humanitarian aid provided by the World Food Programme (WFP) in the city of Taiz on September 11, 2023. AFP
A Western diplomat in Yemen confirmed the Huthis' visit, saying that it may take place "today", Thursday, or within the next two days.
Ali Al-Qhoom, a member of the Huthis' political council, also announced the visit on X, formerly Twitter.
Saudi officials did not immediately respond to a request for comment from AFP.
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.
Hundreds of thousands of people have died from direct and indirect causes such as famine in a conflict that has forced millions from their homes and created one of the world's worst humanitarian crises.
A six-month ceasefire that expired last October is still largely being observed but moves towards peace have been slow since a Saudi team visited Sanaa in April.