The visit is being planned as a separate event from those celebrating the US 250th anniversary celebrations, according to the official.
Trump has often spoken fondly of the UK, British culture and the monarchy, and during his recent visit described King Charles as “my friend”.
The White House official provided no further details on when the visit could take place or what it would entail.
The royal invite was first reported by the Telegraph.
Citing a source close to Trump, the Independent newspaper reported that the invitation could alternatively be extended to Prince of Wales and Catherine, Princess of Wales.
Speaking alongside the US president earlier this week, King Charles also spoke glowingly of the the “special relationship” between the US and the UK.
“I have always admired the ingenuity of the American people and the principles of freedom, which your great democracy has represented since its inception,” he said.
“Throughout my life, from the very first visit to the United States in 1970 – and there were 20 visits since that time – I have cherished a close tie between the British and American people,” King Charles added.
The king’s mother, Queen Elizabeth, made five state visits to the US, beginning in 1957 with President Dwight D Eisenhower.
During the Queen’s last visit to the US in 2007, former President George W Bush famously made a gaffe during the six-day visit, confusing dates and telling her she “helped our nation celebrate its bicentennial in 17 – in 1976”.
After the Queen looked at him, Bush joked that she “gave me a look that only a mother could give a child.”
In an earlier visit with President George HW Bush in 1991, Elizabeth spoke from behind a tall podium on the White House lawn, with only her purple and white hat visible from behind the microphone.
“I do hope you can see me today from where you are,” she told members of Congress at a separate event later in the visit.