DETROIT – Elliott Management made the unsolicited bid in a Monday letter to Compuware’s board of directors, offering to acquire the software and services company for $11 per share, or $2.3 billion.

But Compuware is under intense pressure from investors to fix its business and cut employees that could persist even if an attempted takeover by a New York hedge fund is unsuccessful, the Detroit Free Press reported.

Any change in the ownership of Compuware would be closely watched in Detroit because the company and founder Peter Karmanos Jr. have been huge boosters to downtown. Compuware’s move of its headquarters from Farmington Hills to Campus Martius in Detroit in 2003 was a major catalyst in the revitalization of downtown. Compuware, Michigan’s largest technology company, now has close to 2,000 employees in the city.

In a brief statement, Compuware acknowledged its board of directors received the takeover proposal and will consult its financial and legal advisers. But in an e-mail to employees, CEO Robert Paul said the board believes the company is worth far more than what’s being offered.

The hedge fund, which holds 8 percent of Compuware’s stock, offered a 15 percent premium over the company’s $9.53 closing price last week. Elliott claims that price was “substantially inflated” from publicity over a U.S. Securities and Exchange Commission?s filing in late November, when Elliott started buying additional shares.

Compuware stock closed up 12.9 percent at $10.76 Monday, its highest mark since May 2011.

Jesse Cohn, a portfolio manager for the hedge fund, told the Free Press that Compuware could benefit from large-scale changes of how it does business. However, it is too early to know for certain what those changes would be.

“Compuware has some incredibly good technology, but for years it’s been underperforming,” Cohn said in a phone interview. “It just hasn’t been run that well, and we feel there’s just an incredible opportunity for it to be taken private and to be fixed.”

Earlier this month, another hedge fund and Compuware shareholder, Sandell Asset Management , told Compuware’s board of directors that it must reorganize the firm’s business plan or face the nomination of a slate of replacements.

Sandell, which says it owns 2.5 percent of the stock, said Compuware is less profitable and productive than similar software companies, due in part to its “bloated workforce” and “lack of aggressive cost management.”

According to Sandell, Compuware generates about $212,000 in revenue for each employee, while other software firms average around $317,000 to $334,000 in revenue per employee. The hedge fund suggested several big changes, including spinning off parts of Compuware, trimming redundant personnel and more worker outsourcing.