The country approved an Islamic banking law in May and has been working to amend its legislation to attract foreign investment and stimulate its private sector following last year's war that ousted Muammar Gaddafi.
Asked when Libya might be able to start implementing the rules, he said: "Hopefully very soon. Hopefully this year."
He said the authorities envisaged several options for Islamic banking services. One would be to allow conventional banks to open branches or windows for Islamic finance; another would be permitting conventional banks to become Islamic. Libya is also looking at introducing a special licence for Islamic banking, he said.
The licensing option is still under discussion because authorities have yet to agree on capital requirements, he added.
Apparently for ideological reasons, Gaddafi did not support the development of Islamic banking, which follows religious principles such as bans on interest and pure monetary speculation.
Libya's banking system under his regime was dominated by a few state-owned institutions; most ordinary Libyans did not use credit cards and
their banking services were largely limited to basic cash deposits and withdrawals, making it easier for Gaddafi to keep control over the economy and society.
The country's new authorities want to develop the financial sector and the central bank has been looking to update a 2005 banking law which first allowed foreign banks into Libya.
Asked whether planned changes to the law might mean that Libya would start awarding new foreign bank licences soon, Elkaber said that topic was under assessment.
"We asked the World Bank to do a financial sector review - they sent the first draft and we need to review it. Then we will decide," he said. "But Libya will be an open market anyway, for everyone."