The plans could involve raids by Special Operations and conventional infantry troops, the Post reported on Saturday, citing US officials.
Whether President Donald Trump would approve any of those plans remains uncertain, according to the Post.
The Trump administration has already deployed Marines who arrived in the Middle East on Friday and is planning to send thousands of soldiers from the US Army's 82nd Airborne to the region.
Meanwhile, Yemen's Iran-aligned Houthis launched their first attacks on Israel since the start of the conflict.
Speaking before the strike, Secretary of State Marco Rubio said the US expected to conclude military operations within weeks.
The Houthis said they would continue their operations until the "aggression" on all fronts ended.
Iranian President Masoud Pezeshkian spoke to Pakistan's Prime Minister Shehbaz Sharif, whose government will host a meeting with the Turkish and Saudi foreign ministers on Sunday, seeking to ease regional tensions.
But there's no sign of an immediate diplomatic breakthrough and the war, launched with US and Israeli strikes on Iran on February 28, that's spreading across the Middle East, killing thousands and hitting the world economy with the biggest-ever disruption to global energy supplies.
Israel said it had carried out a wave of attacks on Tehran, targeting what the military said were infrastructure sites belonging to Iran's government.
It also hit targets in Lebanon, where it has resumed its war against Iran-backed Hezbollah, killing three Lebanese journalists in a strike on a media vehicle, Lebanon's Al Manar TV reported, as well as a Lebanese soldier. A follow-up strike on the rescue workers sent to assist them also caused fatalities.
Israel's military said it had targeted one of the journalists, whom it called a "terrorist", accusing him of being part of a Hezbollah intelligence unit, and saying he had reported on locations of Israeli soldiers.
Iran kept up attacks on Israel and several Gulf states after hitting an air base in Saudi Arabia on Friday and wounding 12 US military personnel, two of them seriously, in one of the most serious breaches of US air defences so far.
Washington has dispatched two contingents of thousands of Marines to the Middle East, the first of which arrived on Friday on an amphibious assault ship, the US military said.
The US could achieve its aims without ground troops, Rubio said on Friday, but acknowledged it was deploying some to the region so Trump would have "maximum" flexibility to adjust strategy as needed.
The Pentagon is also expected to deploy thousands of soldiers from its 82nd Airborne Division.
Israel, which regularly faced missile attacks from the Houthis before the war, confirmed a missile had been fired at it from Yemen.
The attack pointed to a potential new threat to global shipping, already hit by the effective closure of the Strait of Hormuz, the conduit for about a fifth of global oil and liquefied natural gas supplies.
Houthi military spokesperson Yahya Saree later said the group carried out a second attack on Israel in less than 24 hours using missiles and drones, and vowed to continue military operations in the coming days.
The Houthis have shown an ability to strike targets far beyond Yemen and disrupt shipping lanes around the Arabian Peninsula and the Red Sea, as they did in support of Hamas in the Gaza war.
If the Houthis open a new front in the conflict, one target could be the Bab al-Mandab Strait off the coast of Yemen, a chokepoint for sea traffic towards the Suez Canal.
With midterm elections due in November, the increasingly unpopular war has weighed on President Donald Trump's Republican Party and he has appeared eager to end it soon, while also threatening escalation. Demonstrators took to city streets across the US on Saturday in anti-Trump rallies described by organisers as a call to action against the war on Iran.
Financial markets have reacted with alarm to signs the war may drag on. The Brent crude oil benchmark is up more than 50 per cent since the war began.
Trump has threatened to hit Iranian power stations and other energy infrastructure if Iran doesn't open the Strait of Hormuz.
But he has extended a deadline he had imposed for this week, giving Iran another 10 days to respond.
Iranian threats to attack ships in the strait have kept most oil tankers at bay. A few vessels have traversed the strait without issue, including ships under the flags of Pakistan and India, after Iranian assurances of safe passage.
Iran has agreed to allow an additional 20 Pakistani-flagged vessels to pass through the strait, with two ships permitted to transit daily, Pakistan's Foreign Minister Ishaq Dar said.
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