President Abdel Fattah al-Sisi had asked parliament last week to approve defending its Gulf Arab ally and the world's biggest oil exporter if Riyadh requests help against the Houthis, whose advances also threaten the strategic Bab el-Mandeb Strait - a gateway to Egypt's Suez Canal.
Egypt has frequently condemned Iranian and Iranian-backed attacks on Gulf countries but has not publicly engaged in direct combat or joined the Mecca mutual defence pact between Saudi Arabia, Pakistan and Turkey that was signed in August.
Foreign Minister Badr Abdelatty said this month that Egyptian membership in the pact remains "under serious consideration."
Egypt, the Arab world's most populous state with one of the region's largest militaries, joined the Saudi-led coalition in an earlier phase of Yemen's war in March 2015 mainly as a naval partner, sending warships to secure Red Sea shipping lanes while pledging air support. It also deployed around 800 ground troops but played only a limited combat role.
Egypt was involved in a costly military intervention in Yemen in the 1960s and has not undertaken a large-scale foreign ground deployment since the 1991 Gulf War.
Saudi Arabia is a major political and financial partner of Cairo, providing billions of dollars in aid, deposits at the central bank and energy supplies under Sisi.
Fighting between the Saudi-led coalition backing Yemen's internationally recognised government and the Houthi militia, which controls the capital Sanaa, has escalated in recent weeks, becoming a volatile front in the US-Israeli war on Iran.
The Houthis have attacked Riyadh's international airport and the state oil giant Saudi Aramco, disrupting flights and oil exports, while aid agencies have warned of worsening conditions in Yemen, already suffering one of the world's worst humanitarian crises.
Abdelatty and Egyptian intelligence chief Hassan Rashad travelled to Riyadh on Wednesday to deliver a letter to Saudi Crown Prince Mohammed bin Salman from Sisi, who said Egypt's support would be limited to defending Saudi territory and borders rather than attacking Yemen. Abdelatty said after that visit that Cairo advocates exploring "every opportunity" to resolve the Yemen conflict diplomatically.
The Saudi crown prince visited Sisi in Cairo on September 15 to discuss security and navigation in the Red Sea after the fighting in Yemen reignited.