"The great interest investors have shown during the roadshow and the bookbuilding process allows us to close the offer sooner than originally planned," Chief Executive Klaus Deller said in a statement.

The offering, which could raise up to 4.21 billion euros (3.7 billion pounds), is easily the largest in Germany this year. Owner Heinz Hermann Thiele and his family are selling a 30 percent stake.

The price range for the shares on offer has been set at 72 to 87 euros per share, reflecting a potential valuation of 11.6 to 14 billion euros for the company. The banks handling the transaction said order books were already covered a week ago.

The offer price, the number of offer shares and their allocation will be set on Wednesday, Knorr-Bremse said.

Listing and trading of the shares on the regulated market of the Frankfurt Stock Exchange is still planned for Oct. 12, with settlement and completion of the IPO planned for Oct. 16.

Deutsche Bank, JP Morgan and Morgan Stanley are acting as joint global coordinators and bookrunners on the deal. In addition, Berenberg, Gossler, Commerzbank, UBS and UniCredit are joint bookrunners.

(Reporting by Douglas Busvine; Editing by Maria Sheahan)