Thyssenkrupp last week dropped plans to spin off its capital goods business after months of shareholder criticism, and opted instead to list elevators, its most profitable division.
Four people familiar with the matter said it was not clear if Kone could fund an all-cash bid and whether or not the deal would face significant anti-trust hurdles similar to Thyssenkrupp's failed steel joint venture with India's Tata Steel.
"Geographical difference in sales could help ease competition concerns," Jefferies analysts wrote in a note.
They said that for Thyssenkrupp an initial public offering of a minority stake in the elevators business probably remained "Plan A" as it would bring in cash more quickly to fund a restructuring of the group, whose products also include steel, bearings and submarines.
Barclays analysts said a deal with Kone would result in 3-4 billion euros of synergies attributable to the German group.
Thyssenkrupp shares have shed 41% in a year while Germany's benchmark DAX index was down 7% over the same period.
On Thursday, Thyssenkrupp shares rose as much as 7.2% to 12.985 euros and were up 2.8% at 0755 GMT.
Shares in Kone were also up 2.8%.
(Reporting by Thomas Seythal; Additional reporting by Linda Pasquini and Boleslaw Lasocki in Gdynia. Editing by Jane Merriman)