The school bus drivers’ union and Durham School Services weren’t able to reach a deal this week, but it sounds as if that could happen next week.

The company’s spokeswoman, Carina Noble, released a statement Friday saying it had made “very good progress in discussions with the union, but still need additional time to fine-tune some details.”

Talks between the Teamsters Local 509, which represents drivers in Charleston County and Dorchester District 2, and the company will resume next week, and the union has promised the company not to strike while discussions are ongoing.

“We appreciate the patience of our employees, our customers and the communities we serve as we work through the bargaining process,” Noble said.

Durham is the company that employs and pays the bus drivers, and it has been working on a new employment contract with the union since last July. Union drivers in Charleston County and Dorchester 2 have authorized their leadership to call a strike if necessary.