Shahristani is likely to become deputy for energy, a new position under the pending government of Iraqi Prime Minister Nouri al-Maliki, The Wall Street Journal reports.
Sources told the newspaper the minister would take the post provided he could play an active role in the Iraqi energy sector. That holds even if Maliki hands the Oil Ministry over to his rivals.
Abdul Hadi al-Hassani, a leader in Maliki's Dawa Party, said the move had the backing of many of the Shiite members of the new Iraqi government, the Journal adds.
Shahristani told Emirati newspaper The National in March that he didn't want to have another term in office, however.
"I wouldn't try to stay unless I was forced to stay," he said from Vienna. "It wouldn't be my wish."
Shahristani faced challenges to his authority by Kurdish leaders who continue to strike oil deals in defiance of his ministry.
Lawmakers called the minister in for questioning most recently in 2009, when he was asked about alleged corruption and declines in oil revenue.