Omani officials declined to comment on the visit, but the Al-Shabiba daily said the three-day trip would see Cheney meeting officials to discuss Iran’s nuclear programme, as well as the situation in Iraq and the Palestinian Territories.
Cheney left Australia on Sunday after a week-long tour of the Asia Pacific region.
In Sydney, he warned Iran that while Washington favours a diplomatic approach it refuses to rule out the use of force to prevent the Islamic republic from obtaining nuclear weapons.
"It would be a serious mistake if a nation like Iran were to become a nuclear power," Cheney warned. "All options are still on the table."
The International Atomic Energy Agency (IAEA) has issued a report saying that Iran had not halted, and in fact had expanded, its uranium enrichment programme, defying a UN Security Council demand to stop by last week.
Iran says its nuclear programme is purely peaceful and aimed at generating electricity.
Last December, Oman and Saudi Arabia expressed their support for a peaceful resolution of the Iran nuclear crisis.
