A US -backed, Saudi-led military coalition is fighting against the Houthis on behalf of the government of President Abd Rabu Mansour Hadi, who lives in exile in Riyadh.
"I hope that there will be a way to avoid the military confrontation in Hodeida", Guterres told reporters.
The United Nations fears that a battle in Hodeidah could be devastating for the estimated 600,000 people still living in the city.
After briefing the security council on Monday, UN humanitarian chief Mark Lowcock told reporters that "if for any period Hodeidah were not to operate effectively the consequences in humanitarian terms would be catastrophic".
The coalition backing Yemen government troops has been closing in on Hodeidah after accusing Houthi rebels of smuggling weapons through the port.
"The meetings will address the brotherly relations between Yemen and the UAE and the joint efforts pertaining to the Arab coalition, led by Saudi Arabia, to liberate remaining Yemeni territory from the control of the Houthi militia that is supported by Iran", reported Saba.
His efforts to convince the rebels to hand over control of Al Hodeidah to UN-supervised global forces had failed, according to reports.
Sputnik Faisal Al Shabibi Yemeni Houthi Rebels Shell Government Forces- Reports
Griffiths is working on a peace plan that involves the Houthi rebels giving up their ballistic missile arsenal in return for an end to Saudi-led air strikes and a political roadmap, ultimately paving the way for a transition out of the crisis.
The UN has warned the Saudi-led coalition that a military attack or siege on the city, long a target in the war, could lead to the displacement of 250,000 people.
US Secretary of State Mike Pompeo on Monday called on all parties "to honour their commitments to work with the UN".
Britain has urged the UAE not to press ahead with an assault on Yemen's main port following United Nations warnings that the attack could leave hundreds of thousands dead in a country already on the brink of starvation.
More than 22 million people are now in serious need of aid, with 8.4 million on the brink of starvation, the United Nations has said.
More than 10,000 Yemenis have been killed since the war began, tens of thousands have been wounded, and another two million people have been displaced.
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The successful bid also comes as President Donald Trump is engaged in public feuds with the leaders of both those countries. Large votes are often swayed by small concessions promised to the right number of smaller nations or by regional biases.