President William Ruto's government opted for government-to-government oil supply contracts, after the East African nation's shilling currency tumbled through a series of record lows.
"The bids opened yesterday and the government is in the course of reviewing them," said Daniel Kiptoo, the director general of energy industry regulator, EPRA.
The winner will supply products for nine months, he said, and will be paid every six months.
"By doing that we alleviate the pressure by removing a third of the demand for dollars in the market," Kiptoo said, referring to oil importers accounting for one-third of monthly demand for hard currency.
The previous system was open to all retailers in Kenya, with the winner supplying the industry for two months and paying for the cargo in hard currency within five days of delivery.
The government is targeting Gulf-based oil exporters like UAE's ADNOC and Saudi Aramco, said Moses Kuria, the minister of trade, in a TV interview.
"We are trying to restructure the way we transact oil between GCC and Kenya so we can ease the pressure on our foreign exchange rate," he told CNN Arabic.
Local oil firms were not immediately available for comment.
The plan was not likely to work since it amounted to just postponing the demand, a foreign exchange trader with a leading commercial bank in Nairobi told Reuters last week.
Kenya's useable foreign exchange reserves have shrunk to less than enough to cover four months of imports of all kinds, which is a statutory requirement. They stand at $6.60 billion or 3.69 months worth of import cover.
Oil prices account for a significant part as international benchmark Brent is above $80 a barrel, even though it has dropped from a peak of $139 in March last year.