Saudi Arabia and the United Arab Emirates last year led a group of Arab states in an embargo against Qatar, accusing the country of being too close to Iran and of funding terrorists. Qatar denies that it supports terrorism.
Pompeo told Saudi Foreign Minister Adel Al-Jubeir on Saturday that the dispute needs to come to a close, the Times said, citing an unnamed senior State Department official.
The administration of President Donald Trump regards the spat between the Arab nations as a distraction while it tries to tackle what it sees as bigger problems, including an increasingly likely confrontation with Iran.
Pompeo is also in the Middle East to discuss the Iran nuclear accord, which Trump is widely expected to scrap this month. Under that 2015 deal, Iran agreed to limit its nuclear energy program in exchange for an end to sanctions that have crushed the country's economy.
The Iran pact was signed by most of the world's major powers. This week, President Emmanuel Macron of France and Chancellor Angela Merkel of Germany separately visited Washington to try to persuade Trump to preserve the accord.