LeBeau, a driving force behind Pittsburgh's dominant defenses, has given the club strong indications he will return, but wants to take the weekend to fully consider the decision.
LeBeau told the club he will give them a final decision early next week, and the Steelers are hopeful he will be back for another season.
"It looks very positive," said one source with knowledge of the situation.
After the loss to the Green Bay Packers in Super Bowl XLV, the Steelers blocked the Arizona Cardinals from interviewing linebackers coach Keith Butler for their defensive coordinator position. Butler is believed to be the team's top choice follow LeBeau as coordinator.