Zelensky, in an interview with broadcaster Fox News on Tuesday, said Trump had agreed to issue the license and that he had subsequently met with representatives of the US defense manufacturing sector.
"He agreed to give us the license, and then I held a meeting with representatives of the production sector, very important American defense companies," Zelensky said.
"I hope we will launch joint production," he added.
The White House did not immediately comment on the statement.
Patriot systems are considered a key, fully effective tool for Ukraine's armed forces in defending against Russian ballistic missiles.
Zelensky had already warned in the spring of critical shortages of ammunition for the launchers, a shortfall compounded by the depletion of global stockpiles linked to the United States' conflict with Iran.
Asked about the battlefield situation, Zelensky said Russian President Vladimir Putin no longer held the upper hand.
"The initiative is no longer in the hands of Putin," Zelensky said. "He is losing 30,000 soldiers a month ... These are big losses, but he does not want to end this war."
Zelensky said Kyiv had repeatedly called for a ceasefire to give diplomats time to pursue negotiations, but that given Moscow's resistance, Ukraine needed to maintain a firm stance and was counting on the effectiveness of international sanctions.
(jh/gs)
Source: PAP