However, the White House is yet to confirm the call and the invitation.
It comes as ties between Japan and China have been strained, ramping up tensions in the region.
The US, a close ally of Japan, is seeking to strengthen its ties with Tokyo but also stabilise its relationship with Beijing ahead of a likely trip by Trump to China in April.
Beijing staged two-day military exercises in the waters off Taiwan this week. Takaichi infuriated China late last year when she said Chinese military action against Taiwan could be grounds for a Japanese military response, breaking away from former Japanese leaders' strategic ambiguity on the highly sensitive matter.
In a statement, the Japanese foreign ministry said Takaichi and Trump agreed to co-ordinate for the visit to happen in the northern spring.
Kyodo News, Japan's news agency, suggested Takaichi's trip could coincide with the annual cherry blossom festival in Washington.
The foreign ministry said the two leaders affirmed that they would "carve out a new chapter in the history of the Japan-US alliance" in a year when the US celebrates the 250th anniversary of its founding.
Takaichi and Trump also agreed on their commitment to promoting co-operation among like-minded partners, including the Japan-US-South Korea partnership, and to a free and open Indo-Pacific, the foreign ministry statement said.
The two exchanged views "mainly on the Indo-Pacific region," the ministry said, but it did not provide details, including whether the two discussed recent actions by Beijing in the region.
Trump met Takaichi in Tokyo in October, shortly after she took office. The two exchanged warm words, and Trump took her with him when he spoke to US troops aboard an aircraft carrier in Japan.
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