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China's overture appeared aimed at deepening engagement with the influential young couple, who played a role in the first summit between Trump and Chinese President Xi Jinping in April, which set an improved tone for relations between the world's two biggest economies.
Kushner, a senior adviser who entered the White House with no government experience, has been assigned the job of conducting Middle East peace diplomacy and will visit the region this week for talks with Israeli and Palestinian leaders.
Helping to manage relations with China is another part of his foreign policy portfolio.
At the same time, Kushner has come under heavy scrutiny, with high-profile investigations into alleged contacts between current and former Trump aides and Russian officials.
No further details were available on the Chinese invitation, which was first reported by Bloomberg News and confirmed by a White House official on condition of anonymity. The Chinese embassy in Washington did not immediately respond to a request for comment.
Speaking at a daily news briefing in Beijing on Wednesday, Chinese Foreign Ministry spokesman Geng Shuang said he had seen reports of the visit but that he was not aware of any details.
Trump railed against China, especially its trade practices, during the presidential campaign. A fence-mending phone call in February was arranged by Kushner and China's U.S. ambassador, Cui Tiankai, U.S. officials said, after Cui invited Ivanka Trump to the Chinese embassy's Lunar New Year reception, where her daughter sang in Mandarin.
Kushner helped plan and attended the U.S.-China summit at Trump's Mar-a-Lago resort in April.
Trump has since had warm words for Xi, praising him for cooperation with efforts to rein in Beijing's nuclear-armed neighbor North Korea. But analysts question how long rapprochement can last if North Korea continues its nuclear and missile development in defiance of international pressure.