The Saudi-backed government and the Huthi rebels have shown a "renewed commitment" to work on a political solution to end a war that has driven millions to the brink of famine, Martin Griffiths told the Security Council.
"With this in mind, I intend to reconvene the parties shortly and to do so in Sweden," he said. "I believe we are close to resolving issues to make this happen."
"I have received firm assurances from the leadership of the Yemeni parties ... that they are committed to attending these consultations. I believe they are genuine."
Griffiths plans to travel to the rebel-held capital of Sanaa next week to finalize arrangements and offered to travel with the Huthi delegation to Sweden "if that's what is needed."
The Saudi-led coalition fighting in Yemen has agreed to "logistical arrangements" to pave the way for talks including medical evacuations out of Sanaa, he added.
Griffiths announced he was close to reaching a deal on an exchange of prisoners and detainees, in a further confidence-building measure ahead of planned talks.
The United Nations had announced talks in Geneva in September that never materialized after the Huthis put forward last-minute demands.
The Saudi-led coalition has been waging a war in Yemen since March 2015 to push back the Iran-backed Huthis and restore to power Yemeni President Abedrabbo Mansour Hadi, whose government is recognized by the United Nations.
Pressure to end the Saudi-led military campaign has grown following the killing by Saudi agents of journalist Jamal Khashoggi, which sparked global outrage.
Back from a visit to Yemen, the head of the UN World Food Programme warned that the country faces a full-blown famine in about six months because of the economic collapse from the war.
"What I have seen in Yemen this week is the stuff of nightmares, of horror, of deprivation, of misery," David Beasley told the council. "Children are already dying."
Eight million people are affected by severe food shortages, according to UN officials, who warn that up to 14 million -- or half of Yemen's population -- are at risk of famine.
"This is a crucial moment for Yemen," Grffiths said of the talks in Sweden, warning that a flareup of fighting on the ground could derail the peace effort. No date for the talks was announced.