The city is controlled by Houthi rebels fighting a Saudi Arabia-led coalition, which believes the port has been key to the rebels smuggling in arms.
Meanwhile, the U.S. was following developments in Yemen very closely, said Secretary of State Mike Pompeo. He estimates that over a million people live in the greater Hodeidah area which is expected to be targeted in the offensive.
"Our top priority is helping to ensure the 22 million Yemenis who need some form of humanitarian aid and protection receive the assistance they need", Grande said last week.
The United States warned Monday that aid must flow through the Yemeni port of Hodeida amid reports that Emirati forces plan to seize it from Huthi rebels.
UN Secretary General Antonio Guterres said there were "intense negotiations" by Griffiths with Yemen's rebel Houthis, Saudi Arabia and the United Arab Emirates to find a "way to avoid the military confrontation in Hodeida".
But he urged them to support United Nations peace efforts.
After briefing the Security Council on Monday, U.N. aid 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 Emiratis have informed us today that they will now give a 3-day grace period for the United Nations (and their partners) to leave the city", it said.
"We are hoping for the efforts of the special envoy to bring a positive resolution".
Yemen has been embroiled in a civil war pitting the coalition against the Iran-backed Houthis since March 2015. The coalition aims to restore the government of self-exiled President Abed Rabbo Mansour Hadi.
According to the United Nations Office for the Coordination of Humanitarian Affairs, an attack could cost as many as 250,000 people "everything - even their lives", and humanitarian organizations have warned that damage to the port, which accounts for the vast majority of the country's food and fuel imports, could tip Yemen into a long-warned-of starvation.
The conflict has left almost 10,000 people dead in Yemen, already the Arab world's poorest country. Malnutrition, cholera and other diseases have killed or sickened thousands of civilians over the years.