UN Humanitarian Co-ordinator Jamie McGoldrick told the BBC that he hoped to receive clearance within hours.
The coalition closed Yemen's borders two weeks ago after rebels fired a missile at the Saudi capital, Riyadh.
But the UN warned the restrictions could trigger "the largest famine the world has seen for many decades".
Yemen is reliant on imports for more than 80% of its food, and it faced the largest food security emergency in the world even before the blockade was tightened.