After meeting behind closed doors for several hours on Monday, the group is scheduled to resume talks on Tuesday.
Mike Ruffin is the only candidate the board is looking at. Interim county manager Wendell Davis said he does not want the job.
Ruffin was fired in September by a 3-2 vote. After November's election, only one opponent remains on the board.
Philip Cousin said he does not regret his decision to fire Ruffin, but is open to talks.
"I will reconsider what is in the best interest of all the citizens of Durham County," Cousins said following Monday's closed-door session.
The two new commissioners said they are weighing all the evidence, as well.
"I just make decisions based on all the information I can gather and I'll wait until I've gathered all the information," commissioner Lewis Cheek said.
Ruffin said he would take the job back if it was offered.
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