By Christoph Steitz, Arno Schuetze, Tom Käckenhoff and Edward Taylor
Letters asking for expressions of interest for the unit, valued anywhere between 12 billion and 17 billion euros (£11-£15 billion), were sent out to private equity and strategic investors, three people familiar with the matter said.
Recipients included private equity groups KKR, Bain, Advent, CVC, EQT, Blackstone, Partners Group and Apollo as well as rivals Kone, Schindler, Otis and Hitachi, the people said.
The parties declined to comment or were not immediately available for comment.
Sources had told Reuters last week that Thyssenkrupp had launched a formal auction process in addition to plans for an initial public offering (IPO), adding chief executive Guido Kerkhoff might be forced to sell the whole unit.
They said consortia were already being formed.
Interested parties are expected to respond to the letters within two weeks, the people said. One person said that Thyssenkrupp was seeking to keep a stake of more than 25% in the unit and expected to sign a deal by year-end.
"We have clearly stated that, in addition to preparing for the IPO, we are also examining expressions of interest from potentially interested parties," a spokesman for Thyssenkrupp said on Wednesday, adding a structured process had been started.
Shares in the group, which are expected to be excluded from Germany's benchmark index this month, rose as much as 5.5% on the news and were up 3.5% at 1556 GMT.
Elevator Technology is by far Thyssenkrupp's most profitable division and a sale could give the cash-strapped group enough ammunition to fix its other struggling business, including plant engineering, steel and car parts.
Thyssenkrupp, suffering from four profit warnings and two botched restructuring attempts, is under pressure to rake in fresh cash due to a weakened balance sheet that has come under pressure following recent rating downgrades by S&P and Moody's.
Thyssenkrupp will have to weigh valuation against speed and execution certainty, the sources said.
They added that strategic players were likely to offer a higher price due to expected synergies, while possible antitrust issues may complicate a deal.
After a failed joint venture deal with Tata Steel, Thyssenkrupp does not want to have another deal scuppered by regulators, they said, adding private equity buyers are not expected to face antitrust scrutiny.
The sales price will, however, also depend on factors like job and site guarantees, which employee representatives are expected to press for, they added.
(Additional reporting by Tassilo Hummel; Editing by Michelle Martin)
By Christoph Steitz, Arno Schuetze, Tom KÃ¤ckenhoff and Edward Taylor