BAGHDAD, April 12 (Reuters) - Iraqi Prime Minister Haider al-Abadi may appoint Jabar Ali al-Luaibi, a former head of state-run South Oil Company, as oil minister in a planned cabinet overhaul that aims to fight graft, a political analyst and local media said on Tuesday.

Luaibi is on a list that Abadi may present later on Tuesday to the parliament, Sajad Jiyad, managing director of the Bayan Center, an Iraqi think tank, told Reuters via Twitter messaging.

The al-Ahd television, an Iraq channel close to a powerful Iranian-backed Shi'ite militia, reported the same information.

The Prime Minister's office declined to comment.

Basra-based South Oil produces most of Iraq's crude.

Abadi presented a first line-up of candidates to parliament on March 31 and asked the MPs to accept, reject or modify it.

Lawmakers then said they would take up to 10 days to respond amid discontent in the dominant political blocs that they did not have a say in choosing the candidates.

Parliament met on Tuesday morning and plans to reconvene in the afternoon possibly to vote on Abadi's new list of candidates.

(Reporting by Maher Chmaytelli) ((maher.chmaytelli@thomsonreuters.com; +9647901917030;))