FRANKFURT — Volkswagen is considering replacing Matthias Müller as chief executive, the German carmaker said in a brief statement on Tuesday.

The move would cap a tumultuous time in charge for Mr. Müller, who took over at the company after it admitted in September 2015 that it had cheated on diesel emissions tests.

Mr. Müller, an auto manager of the old school who spent his entire career at Volkswagen and its subsidiaries, struggled to move the company beyond the scandal, which was costly both to its reputation and to its bottom line.

He steadfastly denied any knowledge of the illegal software, installed in 11 million Volkswagen diesels, that played a major role in creating a serious air pollution problem in Europe.

But he was a high-ranking executive involved in product development at the same time that Audi and Volkswagen were concocting the illegal software and deploying it in vehicles. Mr. Müller also worked closely with some of the people under investigation over possible involvement in the emissions cheating conspiracy.

In a statement, Volkswagen said it was considering “a further development of the management structure of the group,” which could “include a change in the position of the chairman of the board of management.”