"The main topic of discussion is Tomahawks. Of course, there is also the issue of Patriots," the source said, referring to US air defence batteries.
The Ukrainian leader plans to arrive in Washington on Thursday ahead of the talks, the source added.
Relations between the two leaders have warmed since February, when they sparred during a now infamous televised meeting at the White House.
Trump has since grown more hostile towards Moscow, showing mounting frustration with Russian President Vladimir Putin, while expressing sympathy for Ukraine.
The senior Ukrainian source told AFP that the tone of rhetoric between the White House and Kyiv was now "very businesslike."
"It seems that the Americans in general understand that helping Ukraine gives them points, and that, like pressure on Russia, will work to end it all," the source told AFP.
Senior Ukrainian officials visiting the Washington this week met with representatives of US weapon manufacturers, including Raytheon, which produces Tomahawk missiles.
Zelensky will also meet with arms makers to discuss when deliveries could begin, the source said.
"But they need a political signal," it added.
Tomahawk cruise missiles have previously primarily been fired from sea-based launchers, like warships or submarines, but the source told AFP that: "There is a technical solution in place for the launch platform."
Russia, which invaded Ukraine in February 2022, has warned that sending the missiles to Ukraine would rupture its ties with Washington and trigger a new round of escalation.
The source declined to disclose how many of the long-range missiles Trump is considering sending to Ukraine, saying only the arsenal would be "enough for Putin to feel it."
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