"State participation is one option," Merz said on Monday at an industry event, days after labour union IG Metall called on Berlin to rescue Germany's largest steelmaker.
"But state participation can also be part of other options. One could imagine a combination," she said, adding it would be possible that the government would take a stake before a third party takes over the business.
"What I want is a long-term solution for Thyssenkrupp."
Last week Economy Minister Peter Altmaier had opposed the idea of the government taking a direct stake, instead favouring support payments to help the industry transition to hydrogen-based steel production.
A spokeswoman for the Economy Ministry confirmed this position, saying new concepts were needed to improve the competitiveness of Germany's steel sector, which has been hit by the coronavirus pandemic as well as cheap Chinese imports.
Thyssenkrupp, whose steel unit likely made an operating loss of about 1 billion euros ($1.2 billion) last year, is also exploring tie-ups with India's Tata Steel, Germany's Salzgitter and Sweden's SSAB, sources have told Reuters.
Armin Laschet, state premier of North Rhine-Westphalia, where Thyssenkrupp is based, said that a state participation was not a priority at the moment.
"Any solution not involving state participations is better because politicians rarely are the better entrepreneurs," he said at the industry event.
Steel workers will stage protests on Friday to further raise pressure.
(Reporting by Tom Kaeckenhoff, Andreas Rinke and Christian Kraemer; Writing by Christoph Steitz; Editing by Maria Sheahan and Edward Taylor)