The two Middle East rivals, which have long backed opposing sides in conflict zones across the region, severed diplomatic ties in 2016.
However Shiite Muslim-dominated Iran and Sunni-majority Saudi Arabia resumed relations last year under a surprise China-brokered deal.
"Saudi Arabia has asked that we organise joint exercises in the Red Sea," the commander of Iran's navy, Admiral Shahram Irani, was quoted as saying by the Iranian news agency ISNA.
"Coordination is underway and delegations from both countries will hold the necessary consultations on how to conduct the exercise," he added, without providing details including a timeline.
Saudi Arabia did not immediately confirm whether it would hold joint military exercises with Iran.
Since November, Yemen's Iran-backed Huthi rebels have waged a campaign of attacks against ships in the Red Sea and the Gulf of Aden in what they say is a show of solidarity with Palestinians during the Israel-Hamas war in Gaza.
The Huthis have been fighting a Saudi-led coalition since 2015, months after they seized the capital Sanaa and most of Yemen's population centres, forcing the internationally recognised government south to Aden.
Saudi Arabia, which has backed the Aden government, has engaged in a delicate balancing act as the world's biggest oil exporter tries to extricate itself from the war on its doorstep.
It did not join a US-led naval coalition to deter Huthi attacks.
Efforts by the kingdom to broker a Yemen peace deal also faltered in the wake of the Huthi attacks on ships.
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