Kohlberg Kravis Roberts, the firm behind some of the best-known private takeovers in history, wants to take itself public soon, according to a published media report.

The private-equity outfit, which was founded in 1976 by Henry Kravis and George Roberts, wants to list itself on the

New York Stock Exchange

in a transaction that could value it between $12 billion and $15 billion, according to a report Sunday on

The Wall Street Journal's

Web site.

KKR plans to tell investors Monday that its shares should be valued at 10 to 12 times 2009 earnings, which are estimated at $1.2 billion, said the

Journal

report, which cited anonymous sources familiar with the matter.

The KKR deal has an interesting twist. The firm will exchange new NYSE-listed shares in itself for shares of its European affiliate, KPE, which is already publicly traded, according to the

Journal

. The new shares will become the only publicly traded shares of KKR and will represent 21% of the company's total value, the newspaper added. KKR doesn't want to sell any more shares to the public, and KPE shareholders must approve the transaction that will take KKR public, the report also said.

The credit crisis that began last summer brought an end to what had been an extremely busy period for private-equity investors, who purchase and sell companies. As it moves to go public, KKR wants to expand its business and become more of a broad asset manager, the

Journal

reported. Plans include larger investments in infrastructure and real estate, mezzanine debt investing and even stock picking, the newspaper said.

Another well-known private-equity player,

Blackstone Group

(BX) - Get Report

, went public last summer, but its stock has been pressured by worries about its earnings stream, the

Journal

noted. Shares closed Friday at $17.01, 43% off their 52-week high of $29.75.

This article was written by a staff member of TheStreet.com.