"There has been a very positive response so far from the United Nations and the UAE," a First Gulf Bank spokesman said. "We want to go back to the Libyan market but we are still waiting for a clear green light to do so."
The Abu Dhabi lender halted its operations in Libya last April to comply with UN sanctions after it opened its second branch in the country.
First Gulf Bank jointly managed the operation with the Libyan government economic and social development fund, each side having provided half of the bank's US$400 million of authorised capital.
The Libyan business was part of an international expansion strategy, with offices also opened in India, Singapore and Qatar.
The UN froze $150 billion worth of Libyan assets held in overseas bank accounts almost a year ago amid sanctions imposed to weaken the regime of Muammar Qaddafi.
He was ousted and killed in August after nearly 42 years of rule. Libya's economy is expected to recover this year amid a rise in oil production, the IMF said last month.
As the holder of Africa's biggest oil reserves, it is producing more than 1 million barrels per day.
"It was only a matter of time before they can unfreeze these assets. Qaddafi is gone," said Sebastien Henin, a portfolio manager at The National Investor in Abu Dhabi.
"Its a good piece of news and once they receive a clear signal from the UN, they may try to develop their operations further."
First Gulf Bank reported a fourth-quarter profit of Dh1.02bn last week, an increase of 18 per cent compared with the same period a year earlier. The lender said it would distribute a cash dividend of Dh1 a share and a free share for every one held for last year.
Seventeen analysts have a "buy" rating on the bank's shares, while none have a "sell" rating, according to a poll by Bloomberg News.