KUNA news agency said on Thursday that Sheikh Sabah Al Ahmad Al Sabah would depart for the United States on Friday and that a meeting with Trump was scheduled for September 7.
The trio and Egypt cut diplomatic and economic ties with Qatar on June 5, imposing an air, land and marine blockade on the country, accusing it of ties to Iran and "extremist groups" as well as interference in their internal affairs.
Qatar denies the claims and accuses the four countries of an attack on its sovereignty.
On Thursday, Qatar's Foreign Minister Sheikh Mohammad bin Abdulrahman Al Thani called on the blockading countries to stop attempting to influence his country's foreign policy.
"There is no [evidence] against Qatar. Qatar never interferes in any country's politics, and doesn't accept others to interfere in our politics," he said at a news conference in Brussels, Belgium.
The US has given mixed signals about its policy on the Gulf crisis.
Trump immediately expressed his support for Saudi Arabia, but some other US officials, including Secretary of State Rex Tillerson, later adopted a more measured tone.
On Wednesday, Trump spoke with Saudi King Salman and urged an end to the dispute.
Riyadh and Doha are both key allies of the US.
Trump chose Saudi Arabia for his first overseas visit as president in May, two weeks before the Gulf crisis erupted.
Qatar is meanwhile home to a huge US airbase, where the forward headquarters of Centcom - the regional command which leads operations against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group - is based.