The report said Saudi Arabia wants any Dorra gas to be pumped through Khafji and then divided between the two countries, and that Kuwait insists it should take its share directly from the field.
Kuwait shares separately with Iran and Saudi Arabia the Dorra gas field, whose recoverable reserves are estimated at some 220 billion cubic metres (seven trillion cubic feet).
Development of the part jointly owned with the Saudis has been frozen for a year, according to Al-Rai.
The row comes a month after production at the offshore Khafji oilfield in a neutral zone between the two Arab states was halted last month, with Kuwaiti officials saying it was due to technical issues.
However, trade unions and media outlets in Kuwait said that Saudi Arabia stopped production unilaterally because of differences between the two countries.
Khafji is capable of producing 311,000 barrels of oil per day.
Kuwait and Iran have been involved in unsuccessful talks for more than 10 years to demarcate their maritime border in the area.
The Gulf emirate is rich in oil but needs the Dorra field because it lacks sufficient supplies of natural gas.