Official documents obtained by Reuters news agency show government lawyers advised the US it might be considered a co-belligerent under international law.
The Obama administration has continued to authorise weapons sales to Saudi Arabia despite the warnings last year.
On Saturday, an air strike on a funeral hall in Sanaa killed some 140 people.
The coalition denied responsibility for the attack, but Washington said it would review its support to "better align with US principles, values and interests".
US President Barack Obama agreed to provide "logistical and intelligence support" to the coalition after it intervened in the conflict between forces loyal to Yemen's internationally-recognised government and those allied to the rebel Houthi movement in March 2015.
Since then, more than 4,125 civilians have been killed and 7,207 injured, the UN says, with air strikes believed to have caused about 60% of the deaths.
The documents detailing US government concerns about the civilian casualties and the potential legal implications for US military personnel were obtained by Reuters under the Freedom of Information Act and date from May 2015 to February 2016.
One document quotes a state department official as telling human rights groups in October 2015 that he believed coalition strikes were "not intentionally indiscriminate but rather result from a lack of Saudi experience with dropping munitions and firing missiles".
"The lack of Saudi experience is compounded by the asymmetric situation on the ground where enemy militants are not wearing uniforms and are mixed with civilian populations," the official said.
"Weak intelligence likely further compounds the problem," he added.
US officials also compiled a list of "critical infrastructure" that should be spared to enable Yemenis to restart commercial access and deliver humanitarian aid.
An email shows state department officials organised a meeting in January to discuss "options to limit US exposure to LOAC [Law of Armed Conflict] concerns."
The Law of Armed Conflict prohibits attacks on civilians and says civilians and civilian objects must be spared from incidental or collateral damage to the maximum extent possible when military objectives are attacked.
Reuters reported that another email made specific reference to a 2013 ruling from the war crimes trial of former Liberian leader Charles Taylor, who was found guilty of aiding rebels who committed atrocities in Sierra Leone during its civil war.
The ruling found that "practical assistance, encouragement or moral support" is sufficient to determine liability for war crimes.
In August, Human Rights Watch and Amnesty International said they had documented more than 70 unlawful coalition air strikes, some of which they believed might amount to war crimes, and 19 attacks using internationally-banned cluster munitions.
The coalition has said its forces have clear instructions not to target populated areas and to avoid civilians, and has dismissed previous allegations of civilian deaths as fabricated or exaggerated.

Top seed Murray, 29, can set up a potential second-round clash with Britain's Slovenia-born Aljaz Bedene if he defeats the world number 49.
Bedene, 26, must first get past France's Benoit Paire after replacing Jo-Wilfried Tsonga in the main draw.
Swiss second seed Stan Wawrinka, 31, plays Spaniard Fernando Verdasco.
British wildcards Dan Evans and Kyle Edmund face France's Paul-Henri Mathieu and eighth seed Gilles Simon respectively.
Elsewhere in the first round, Australian Nick Kyrgios takes on Canadian third seed Milos Raonic and Britain's James Ward meets Luxembourg's Gilles Muller.
Queen's is part of the ATP World Tour 500 series and finishes a week before Wimbledon, which runs from 27 June to 10 July.
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The US government is concerned it could be implicated in potential war crimes in Yemen because of its support for a Saudi-led coalition air campaign.
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British number one Andy Murray will face France's Nicolas Mahut in the Aegon Championships first round at Queen's Club.