The Russian-flagged Arctic Metagaz, carrying 61,000 tonnes of liquefied natural gas, was badly damaged in a suspected sea drone attack near Maltese waters early in March.
It has since drifted off Libya.
All 30 crew members were rescued and put on another vessel heading to the Libyan city of Benghazi, the Libyan Maritime Authority said.
The tanker is part of Russia's so-called shadow fleet transporting oil in violation of international sanctions over Russia's more than four-year-old invasion of Ukraine.
A recent temporary US waiver on those sanctions is aimed at easing supply shortages amid the Iran war.
Russia blamed the attack on Ukrainian sea drones.
Ukraine says the oil export revenue is helping fund Russia's invasion.
The Ukrainian forces, most of them drone experts, operate mainly at an air base in the coastal city of Misrata but also in other military facilities in the capital Tripoli and the coastal town of Zawiya, the officials told the Associated Press.
They spoke on condition of anonymity to discuss confidential matters.
One of the officials said the March 3 drone strike that hit the tanker was launched by Ukrainian operatives in a military facility in Tripoli.
The Libyan Maritime Authority said at the time that the tanker experienced "sudden explosions, followed by a massive fire," while it was about 240km off the Libyan city of Sirte.
The Libyan governmental body mistakenly reported that the tanker had sunk.
The Arctic Metagaz remained afloat after the attack and was pushed by winds and currents toward the Libyan coast, according to the World Wide Fund for Nature.
In recent weeks, Libyan authorities attempted to tow the tanker to a "safe zone" off the country's western coast.
However, their efforts failed due to "harsh" weather conditions and strong winds that caused the tanker to drift "out of control".
Neither Russian nor Ukrainian officials made any immediate comment on the claims.
The Libyan government did not immediately respond to a request for comment.
The officials said Ukrainian forces were gradually deployed in western Libya in recent months as part of what one of the officials described as a "covert deal" between officials in Kyiv and the embattled government of Prime Minister Abdul-Hamid Dbeibah who is based in Tripoli.
The deal enjoyed the backing Ukraine's allies including the United States, whose adviser for African affairs Massad Boulos has drafted a proposal to settle the long-running conflict in Libya, which keeps Dbeibah as prime minister, the officials said.
Boulos' proposal also includes appointing Saddam Hifter, son of powerful east-based military commander Khalifa Hifter, as head of the presidential council, the officials said.
Saddam Hifter is the chief of staff of the self-styled Libyan National Army which controls eastern and southern Libya, incluiding major oil fields.
The country has for more than a decade been split between a United Nations-supported government in Tripoli, now led by Dbeibah, and a rival administration loyal to Russia-backed Hifter in the east.
Each has been backed by different armed groups and foreign governments.
The mandate of Dbehibah's government expired when Libya failed to hold its first presidential election during his watch in December 2021.
Jalel Harchaoui, a Libya analyst with the Royal United Services Institute, suggested that the presence of Ukrainian forces in western Libya is part of NATO's efforts to keep the area "out of Russia's reach".
"It is entirely plausible that, with the knowledge and blessing of NATO powers - chiefly the United States but also the United Kingdom and Turkey - several small groups of Ukrainian operatives now maintain a presence in the greater Tripoli area," he said.
Libya has been wracked by chaos since a NATO-backed uprising toppled then killed authoritarian ruler Muammar Gaddafi in 2011.
