UPDATE 1-Elliott Management offers to buy Compuware for $2.3 bln

Dec 17 (Reuters) - Activist hedge fund Elliott Management Corp offered to buy business software maker Compuware Corp for $2.3 billion, seven months after it pushed for a sale of rival BMC Software Inc.

Elliott's $11 per share offer represents a 15.4 percent premium to Compuware's Friday close on the Nasdaq. Compuware's shares rose to just below the offer price.

"We believe in the quality of Compuware's assets - however, its execution, profitability and growth have meaningfully underperformed," Elliott said in a letter to Compuware's board.

Elliott said on Monday it controls 8 percent of Compuware, which makes software to manage large computer networks.

Elliott, a $20 billion investment firm founded and run by publicity-shy Paul Singer, repeatedly pressured BMC earlier this year to sell itself and appoint new directors.

Compuware filed last week for a possible initial public offering of its Covisint Corp unit, which it said would allow the business to pursue strategic options.

Shares of the company were up 15 percent at $10.95 in late morning trading on Monday on the Nasdaq.