This is reported by CBS News, citing its own sources.
It remains unclear whether the Chinese leader has accepted such an invitation. The spokesperson for the Chinese embassy in Washington declined to comment.
In addition to Xi Jinping, Hungarian Prime Minister Viktor Orban may also receive an invitation to the inauguration. However, CBS News sources claim that the Hungarian leader is "still contemplating" such plans.
"World leaders are lining up to meet with President Trump because they know he will soon return to power and restore peace through American strength worldwide," said Trump's press secretary, Carolina Levitt.
According to CBS News, ambassadors and other diplomats are usually invited to the inauguration, but leaders from other countries have never attended the power transition process in the U.S.