"Around 2,000 have already agreed to leave, and we will likely see a further 2,000 people accept packages," Schaefer-Klug said.
"I'm not worried about meeting the cost targets, the scale of the uptake of buyout offers means it is now a question of whether we have enough staff to manage the current workload," Schaefer-Klug said at a press conference on Friday.
"What is missing is a clear vision for the way forward at Opel in terms of utilized production capacity and job guarantees beyond 2020," he said.
Opel, which PSA bought from General Motors for $2.6 billion, has made losses for almost 20 years, and Tavares has been frustrated in his bid to cut high production costs.
PSA has given Opel until 2020 to return to profit as part of a recovery plan aimed at shifting the brand's model lineup onto PSA's architecture, with the French parent pursuing 1.7 billion euros ($2.1 billion) in savings from its purchase.