UPDATE 1-Compuware, after rejecting Elliott bid, explores sale

(Adds share move, details of sale process)

NEW YORK, Feb 21 (Reuters) - Business software maker Compuware Corp, which has rejected a $2.3 billion bid by an activist investor, is exploring a sale and talking to buyout firms to gauge takeover interest, four people familiar with the matter said.

The Detroit-based company has held early talks with several large private equity firms, including Blackstone Group LP and TPG Capital LP about a potential deal, the people said on Thursday.

Shares of Compuware rose as much as 9.5 percent to $12.74 in Nasdaq trading on Thursday before trimming gains to trade up 2 percent, valuing the company at around $2.5 billion.

Compuware in January rejected an $11 per share offer from New York-based hedge fund Elliott Management Corp, its second-largest shareholder, which holds an 8.7 percent stake, and said it would proceed with plans to spin off a noncore unit, cut costs and pay out dividends.

The company, however, opened the door to a better offer from Elliott or other buyers, and has agreed to provide the investor with confidential financial information to allow for due diligence.

Investment banks Goldman Sachs Group Inc and Allen & Company are advising Compuware on the process, said the sources, who asked anonymity because the process is not public. Goldman, Elliott and TPG declined to comment. Blackstone and Allen & Company could not immediately be reached for comment.

A Compuware spokeswoman declined to comment but pointed to the company's statement on Jan. 25 that said "the board will carefully review and evaluate any credible offer it receives."

Compuware's diverse business lines make it a tough takeover target for industry rivals but private equity firms could be interested in buying the entire company, according to the people familiar with the matter.

(Reporting by Nadia Damouni and Soyoung Kim in New York; editing by Gerald E. McCormick and Matthew Lewis)