Providing such arms to Ukraine would be a shift for Trump, whose campaign worked to amend the Republican National Convention's platform from supporting "lethal defensive arms" to Ukraine to the more vague "appropriate assistance."
A State Department official cautioned that the proposal is unlikely to get approval while Trump is on a 13-day foreign trip to Asia.
The State Department declined to comment on the details of the recommendation.
Kurt Volker, the department’s special representative for Ukraine negotiations, also declined to confirm any final decision.
“Ukraine has been facing a conflict on its own territory for the last three years… it is a reasonable thing for a country to defend itself, and it’s also reasonable for others to help countries defend themselves, as well,” he said.
In an email, National Security Council spokesperson Michael Anton told ABC News, “The U.S. has never ruled in or out lethal aid to Ukraine and we have no announcement at this time.”
Ukrainian officials have been publicly optimistic about relations with the United States.
"We are really satisfied with the acceleration of U.S.-Ukraine relations at the moment," Artur Gerasymov, a member of the Ukrainian parliament and chairman of a military subcommittee, told the publication Foreign Policy in late October.
"This permits me, better informed, to go back and advocate for what I believe you need, as brought to me by your minister of defense and, certainly, your president," Mattis said. "For example, we've just approved -- just very recently, last couple of weeks -- another $175 million worth of equipment, including some specialized equipment that can be used to help defend the country, bringing to a total of nearly $750 million in the last several years."
Mattis also said U.S. military leadership was reviewing the American position on providing defensive lethal weapons.
"I would also point out that, on the defensive lethal weapons... we are actively reviewing it," Mattis said. "I will go back, now, having seen the current situation, and be able to inform the secretary of state and the president in very specific terms what I recommend for the direction ahead."
On the campaign trail, Trump vowed not to weigh in on arming Ukraine and promised a reset in relations with Russia. His campaign created controversy when it intervened in the RNC platform in July 2016 to remove any mention of aiding Ukraine with "lethal arms," contrary to most Republicans' positions.
"They softened it, I heard, but I was not involved," Trump said of his campaign in an interview with ABC News's George Stephanopoulos at the time, before adding, "The people of Crimea, from what I've heard, would rather be with Russia than where they were."
Trump's then-campaign chairman, Paul Manafort, had worked for years for the pro-Russian Ukrainian President Viktor Yanukovych, who was expelled in a popular uprising in 2014.
Russia invaded Crimea and sent troops and arms into eastern Ukraine shortly after his ouster, leading to a conflict that rages on to this day. The Obama administration never provided arms assistance to Ukraine in response.
ABC News' Luis Martinez contributed to this report.