The deliberations put pressure on President Donald Trump, who's fighting perceptions he is soft on the Kremlin amid investigations into whether his campaign colluded with Moscow to interfere in the 2016 US election.
The proposal, endorsed by the Pentagon and the State Department, reflects his administration's growing frustration with Russian intransigence on Ukraine and a broader deterioration in US-Russian ties.
The tensions were seen most recently in Russian leader Vladimir Putin's order for America to eliminate more than half its diplomatic personnel in Russia.
It's not dramatically different from proposals rejected by President Barack Obama, who feared an influx of US weapons could worsen the violence responsible for more than 10,000 deaths in Ukraine since 2014 and create the possibility of American arms killing Russian soldiers.
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Such a scenario could theoretically put the nuclear-armed nations closer to direct conflict.
While Obama was still in office, Trump's campaign also rejected the idea of arming Ukraine, preventing it from being included in the Republican platform.
While there is no deadline for a decision and one is not expected imminently, the debate is going on as US and Russian diplomats prepare to meet as early as this coming week to explore ways to pacify eastern Ukraine, where Russian-backed separatists have fought the central government for three years.
"The Russians have indicated some willingness to begin to talk with us about a way forward on Ukraine," Secretary of State Rex Tillerson said after seeing his Russian counterpart, Foreign Minister Sergey Lavrov, last week in the Philippines.
Russia hawks in the US and uneasy American allies have feared such a prospect since Trump took office after a campaign in which he questioned NATO's viability and repeatedly expressed his wish for a new US-Russian partnership.
At one point, two years after Russia's annexation of Ukraine's Crimea region, Trump even challenged the notion that the Russians would "go into Ukraine.