The German air traffic controllers union says it could stage a walkout later this week.
Union officials said Monday they had rejected the latest management proposal, but are willing to meet with an arbitrator.
The union's leadership says a strike could happen as soon as Wednesday unless a deal is made to change working conditions and increase pay.
The air traffic controllers case was sent to arbitration in August. The union has since rejected a decision.
The German airline Lufthansa said on its website it could not estimate the impact of an air traffic controllers strike, but would try to minimize any inconveniences to passengers.