* Sears Holdings says it may put Sears Canada up for sale
* Sears to hire investment bank to suggest options for its stake
* Sears Canada shares rise nearly 5 percent
(Adds analyst comment, share movement, background)
May 14 (Reuters) - Sears Holdings Corp said on Wednesday that it was considering the sale of its 51 percent stake in Sears Canada Inc, a move that could mean all of the Canadian department store operator goes up for sale.
Shares of Sears Canada jumped 4.7 percent in midday trading, while Sears Holdings, which is controlled by hedge fund billionaire Eddie Lampert, fell 0.8 percent, reversing earlier modest gains.
Sears Holdings, which operates more than 2,300 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.
Desjardins Securities analyst Keith Howlett said that suggested Sears had already decided to exit Canada, but had not yet determined how.
Potential buyers include major landlords and pension funds that want to use mall space occupied by Sears Canada, along with private equity and retail turnaround groups, such as Sun Capital, Hilco and Gordon Brothers, Howlett wrote in a note to clients.
Large-format retailers, such as Macy's Inc and Kohl's Corp, are also potential suitors, he said, as are Canadian operators, such as Hudson's Bay Co, that may want to expand and fend off new rivals.
Sears Canada, which has a market value of C$1.6 billion ($1.5 billion), said it would cooperate with its parent company "to achieve value for all shareholders."
The company has already sold several of its most valuable leases over the past year, including one for its flagship store at Toronto Eaton Center, raising about C$591 million.
The move comes as Sears Holdings, the operator of Sears department stores and Kmart discount chain, tries to engineer a turnaround. Sales have declined since 2005, when Lampert merged the two U.S. chains in an $11 billion deal.
The company has closed about 300 U.S. stores since 2010, but still struggles to generate cash.
Also falling on hard times is Sears Canada, which traces its Canadian roots back to the early 1950s, when it formed a partnership with one-time national retailer Simpsons.
Sales have declined for six straight years as Sears Canada has lost significant market share in the competitive Canadian retail market, where Wal-Mart Stores Inc and Target Corp have been expanding.
Target considered acquiring Sears Canada when it studied expansion into the country, a 2012 British Columbia labor board document showed, but it decided that Zellers stores were more attractive.
Earlier this year, Sears Canada said it would have about 20,000 employees after a string of job cuts, including some 3,000 positions eliminated since November.
Chief Executive Officer Douglas Campbell said last month that the company was not pursuing any asset sales, but would consider opportunities that would "substantially" add value.
Sears Canada has 176 corporate and 234 Hometown stores, 1,400 catalog and online pick-up locations, 97 Sears travel offices and a nationwide repair and service network.
($1 = 1.0905 Canadian dollars)
(Additional reporting by Euan Rocha in Toronto; Editing by Savio D'Souza and Lisa Von Ahn)