A statement said the proposal could send "a powerful message of the will to end the war".
The offer comes a week after drone and missile strikes hit Saudi Arabian oil facilities.
Houthi rebels have claimed to have carried out the attack, but the US and Saudi Arabia have blamed Iran.
Tehran denies any involvement in the strikes.
Yemen's civil war has killed 10,000 and pushed millions to the edge of starvation in what has become the world's worst man-made humanitarian disaster.
Saudi Arabia and its regional allies drastically escalated the conflict in 2015 when they launched an air campaign against the Houthis, who had ousted President Abdrabbuh Mansour Hadi and seized the capital, Sanaa.
The Houthis have launched numerous drone, missile and rocket attacks on the Gulf kingdom.