Hiesinger has perhaps a unique chance to merge his industrial group's European steel operations with those of Tata Steel, but is caught between the interests of shareholders, steelworkers and politicians.
Shareholders including activist investor Cevian, with 15%, would love to see Thyssenkrupp shed the steelmaking activities that are a drag on its valuation to concentrate on capital goods such elevators and car parts.
Read more from our special coverage on "THYSSENKRUPP"
But Thyssenkrupp's powerful works council that represents 28,000 steelworkers, as well as top German politicians, will resist any move that could cost jobs and see the company abandon its 200-year-old steelmaking roots.
German steel and mining workers have particularly strong co-determination rights, under which employee representatives can block major strategic moves, thanks to the key role the industry played in the country's First and Second World War efforts.
"When we believe we have a viable concept, then it will first go to the company's co-determination committees and only then, if we see that something can really occur, would we go to the politicians," Hiesinger said in remarks released on Friday.
"If such solutions are possible we will play an active role from a position of strength," he told reporters. "Whether, when and with whom consolidation may take place is still completely unclear today."
Thyssenkrupp shares, which are at eight-month highs this week, were up 0.5% by 1113 GMT and were the third-biggest gainers in the German blue-chip index.
ArcelorMittal fell 0.6%, while German steelmaker Salzgitter shares were flat.
Thyssenkrupp is Europe's third-biggest steel producer after ArcelorMittal and Tata Steel.
A combination of Thyssenkrupp's steel division with Salzgitter might be politically preferable but Salzgitter's CEO has repeatedly ruled out mergers, while a tie-up with ArcelorMittal would probably run into antitrust issues.
"We think, and always have, Tata is the only option for a Thyssenkrupp demerger of steel," wrote Credit Suisse analysts, who rate Thyssenkrupp "outperform".
Hiesinger cautioned that movement towards consolidation was neither as definite nor as advanced as has been reported in the media.
But with steel prices on the rise around the world for the first time since the financial crisis - due to a combination of factors including measures against the dumping of cheap Chinese steel - he does not have infinite time.
"We believe management must be under some time pressure - if the steel cycle recovers sharply, the rationale for a demerger of steel would be weaker, and a window could have been missed," wrote Credit Suisse.
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