UPDATE 1-Sears Holdings says could sell its majority stake in Sears Canada

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May 14 (Reuters) - Sears Holdings Corp said it was looking to sell its 51 percent stake in Sears Canada Inc and could even put the whole Canadian department store operator up for sale.

Shares of Sears Holdings, controlled by hedge fund billionaire Eddie Lampert, rose 8 percent to $46.48 in premarket trading.

Sears Canada has lost significant market share in intensely competitive Canadian retail market, where Wal-Mart Stores Inc and Target Corp have been expanding.

Sears Holdings, which operates nearly 2,500 stores in the United States and Canada, said it would hire an investment bank to help explore alternatives for its stake in the Canadian company.

The operator of Sears department stores and the Kmart discount chain is trying to engineer a turnaround after suffering from declining sales since 2005, when Lampert merged the two U.S. chains in an $11 billion deal.

Sears Holdings has closed about 300 U.S. stores since 2010, but still struggles to generate cash.

Sears Canada, which has a market value of C$1.6 billion ($1.5 billion), said on Wednesday it would cooperate with its parent company "to achieve value for all shareholders".

Sears Canada has also been closing stores to rein in costs and remain competitive.

Sears Canada's shares, which have risen about 55 percent in the past year, closed at C$15.76 on Tuesday on the Toronto Stock Exchange. Sears Holdings' shares have fallen about 4.5 percent in the past year. ($1 = 1.0905 Canadian Dollars)

(Reporting by Ashutosh Pandey in Bangalore; Editing by Savio D'Souza)