The World Food Program said the fighting could result in up to 1.1 million people being either displaced or trapped within the city and in need of emergency food assistance.
U.N. envoy Martin Griffiths has visited Sanaa and Saudi Arabia to try to negotiate a solution.
The Houthis have indicated they would be willing to hand over management of the port to the United Nations, sources told Reuters. A U.S. official said Washington was urging the Saudis and Emiratis to accept the deal.
"The coalition will achieve its goal of liberating Hodeidah, city & port. Yet we will support all efforts to achieve an unconditional peaceful withdrawal of Houthi gangs," UAE Minister of State for Foreign Affairs Anwar Gargash said in a Twitter post on Saturday.
The Arab states say they must recapture Hodeidah to deprive the Houthis of their main source of income and prevent them from smuggling in Iranian-made missiles, which have been launched at Saudi cities. The group and Tehran deny the accusations.
The coalition has pledged a swift military operation to take over the airport and seaport without entering the city centre, to minimise civilian casualties and maintain the flow of goods.
"The battle for Hodeidah is reaching the point of no return," the International Crisis Group said in a conflict alert.
"This is the final, fragile moment in which it may still be possible for UN-led negotiations to prevent a destructive fight that is likely to exacerbate dire humanitarian conditions and further delay broader negotiations to end the war."
