If it returned, Gabon would be the smallest producer in the Organization of the Petroleum Exporting Countries and bring its ranks to 14 countries following last year's return of Indonesia, which had quit in 2008.
"They sent the request to OPEC officially," said one of the sources, an OPEC delegate.
An oil official in Gabon declined to comment.
Gabon joined OPEC in 1975 and left in 1995 over the exporter group's refusal to grant its request for reduced annual contributions in line with the country's small production, news reports said at the time.
The move to rejoin comes as key OPEC members and outside producers such as Russia are attempting to support prices through a deal to freeze output which will be discussed this weekend in Doha. The initiative has helped oil prices to start recovering from a 12-year low reached in January.
OPEC in 2014 had abandoned its traditional role of cutting supply to support the market, accelerating a drop in prices which were falling due to oversupply and prompting critics to question its relevance.
Gabon produces 200,000 barrels of oil per day (bpd) according to the International Energy Agency, and output is in decline. Last year, the government launched an offshore licensing round in a bid to boost exploration. [nL8N12R24E]
Ecuador, which pumps 530,000 bpd, is currently the smallest OPEC producer.
The next step, the sources said, would be for OPEC oil ministers to discuss Gabon's request. They hold their next meeting in June.
OPEC rules state that a country needs to have "a substantial net export of crude" in order to become a full member. Still, the ministers waived this requirement with the decision to welcome back Indonesia, now a net oil importer.
Whether Gabon's return would be as straightforward is not clear. Indonesia was deemed by OPEC to have "suspended" its membership, while it calls Gabon's departure a "termination" - implying a more formal severing of ties.