Jared Kushner, a New York businessman, is married to Trump’s daughter Ivanka and served as a top campaign adviser.
Kushner is travelling in the Middle East with the chairman of the Joint Chiefs of Staff, General Joseph Dunford.
Other details about the trip are not being released. The official isn’t authorised to speak about confidential meetings by name and demanded anonymity.
The fight against ISIL is likely to top the agenda, AFP news agency reported.
The US is leading an international coalition fighting the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), launching air strikes to assist Iraqi forces on the ground.
Since last month, the forces have been engaged in a grinding battle for west Mosul, sending more than 200,000 civilians fleeing for safety.
Kushner, like his father-in-law, has no previous experience in government but has become one of the most powerful men in Washington.
Valued by Trump for his discretion and loyalty, the baby-faced 36-year-old is officially a White House senior adviser with far-reaching influence over domestic and foreign policy.
Kushner has been deeply involved with presidential staffing and has played the role of shadow diplomat, advising on relations with the Middle East, Canada and Mexico.
Last week he launched a task force meant to modernise government, using lessons drawn from the private sector.
Kushner’s wife Ivanka, the 35-year-old first daughter, also plays a key role in advising the president. She officially became assistant to the president last week, after being a regular presence in the White House since Trump’s election.