A US media outlet says President-elect Donald Trump has invited Chinese President Xi Jinping to his inauguration, but it is not clear whether Xi has accepted the invitation.

CBS News on Wednesday quoted multiple sources as saying that Trump invited Xi to his swearing-in ceremony, which is set to take place in Washington D.C. on January 20.

The media reported that the invitation was sent to Xi in early November, shortly after Trump won the presidential election.

It also said Trump's transition team is considering inviting other foreign leaders to the inauguration as well.

The media said ambassadors and other diplomats are typically invited to inaugurations, but State Department records dating back to 1874 show that no foreign leader has ever attended a transfer-of-power ceremony.

In his incoming administration, Trump has appointed hardliners on China to important positions dealing with diplomacy and security matters.

In an interview with NBC television on Sunday, Trump reflected on a meeting he had with Xi about measures to address drug problems.

He said: "I had an agreement with President Xi, who I got along with very well. We've had communication as recently as this week."