The phone call was made on May 1 during a meeting with a Saudi delegation at the White House, the report added.
"It's Jared Kushner", Yashar Ali of New York Magazine wrote on Twitter.
A White House official said that Kushner and his wife, who are both Orthodox Jews, have received a rabbinical dispensation to join the president aboard Air Force One as he sets off on his first overseas Friday, according to the report.
White House press secretary Sean Spicer said at the time that Kushner was working jointly with the State Department to manage the administration's foreign affairs.More news: Djokovic, Nadal through easily but Murray crashes out in Madrid
For now, it seems to be working, and the deal sealed by Kushner will be formally announced during the president's visit to Saudi Arabia. "It's more normal for them than any previous administration".
"If you can't produce peace in the Middle East, nobody can", Trump told Kushner at a gala a few days before his inauguration.
Lockheed is the only company that manufactures THAAD.
But the military contractor has cut the cost of its products before - in February, Lockheed slashed the price of its F-35 Lightning II fighter jets after negotiations with Trump.More news: Tear-stained apology caps Weiner's guilty plea in sexting case
The gesture, which reportedly impressed the Saudi guests, demonstrates how Kushner, like his father-in-law President Trump, has brought the real estate world's dealmaking practices into high-level White House diplomacy. In March, he was seen at the table when Trump hosted the deputy crown prince, Mohammed bin Salman, at a lunch in the White House's State Dining Room.
Mr Trump met Russian Foreign Minister Sergei Lavrov and Russia's Ambassador to Washington in the Oval Office the day after he fired Mr Comey.
President Trump's visit to Saudi Arabia is expected to focus on how much he likes selling them weapons, and how much he doesn't like Iran, and how great he thinks it'll be if they join together as "Arab NATO", while assuring the U.S. has deep influence over what that alliance does. He will then head on to Israel, Italy, Belgium, and Sicily and will return to Washington D.C. on May 27.More news: China Trade Deal: Commerce Secretary Ross Breaks Down What to Know
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