* 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 up 4 percent, Sears Holdings drops 2.8 percent
(Recasts, adds comments from retail consultants, analyst, HBC, updates stock price)
TORONTO, May 14 (Reuters) - Sears Holdings Corp said on Wednesday it was looking at selling its 51 percent stake in Sears Canada Inc, a move that could trigger a deal for the entire Canadian operation, though a quick and easy sale was seen as unlikely.
Sears Holdings, which operates more than 2,300 stores in the United States and Canada, said it will hire an investment bank to explore options for its share of Sears Canada.
Shares of Sears Holdings, which is controlled by hedge fund billionaire Eddie Lampert, dropped nearly 6 percent on Wednesday while Sears Canada stock rose 3.4 percent.
The move comes as Sears Holdings, which operates Sears and Kmart discount stores, tries to engineer a turnaround.
Sales have declined since 2005, when Lampert merged the two U.S. chains in an $11 billion deal, and the company has closed about 300 U.S. stores since 2010, but still struggles to generate cash.
While such a large package of retail space is rarely available in Canada, industry experts said buyers may be put off by the health and composition of Sears Canada's operation, especially after the sale of leases for some of its most valuable locations.
"The pieces are likely worth more than the whole, particularly as we consider that the Sears brand has been allowed to decay," said Jim Danahy, chief executive of consultancy CustomerLAB and director of the Centre for Retail Leadership at York University's Schulich School of Business.
"This is carrion. The vultures are circling and they're not interested, no one's interested, in the whole thing."
Another Canadian retail analyst said he didn't expect a speedy deal because he didn't see an obvious single buyer for the entire company.
Potential suitors may also be chilled by the frosty reception Canada has given to Target Corp. Last year, Target reported an operating loss of nearly $1 billion in Canada after opening 124 stores and three distribution centers.
"The Target deal has taken the bloom off the Canadian rose," said Danahy.
FALLING SALES, AGGRESSIVE RIVALS
Sears Canada, which traces its Canadian roots back to the early 1950s, has fallen on hard times in recent years as competition intensified in the department store sector.
The company, which said it would cooperate with its parent company "to achieve value for all shareholders," has already sold several of its most valuable leases over the past year, including one for its flagship store at Toronto Eaton Centre, raising about C$591 million ($541.9 million).
Sales have declined for six straight years as Sears Canada lost market share to such rivals as Wal-Mart Stores Inc and Target, which have been aggressively 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.
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.
Earlier this year, the company said it would have about 20,000 employees after a string of job cuts, including some 3,000 positions eliminated since November.
While the bulk of Sears Canada's stores are in smaller and suburban markets, that could still underpin a healthy retail operation, said Antony Karabus, President of Hilco Retail Consulting.
"There is full, significant business volume. Don't for a minute think that there isn't, because there is significant volume in those suburban malls," he said. "There is a real business there, for sure."
Desjardins Securities analyst Keith Howlett said potential buyers could include major landlords and pension funds that want to better use mall space occupied by Sears Canada, along with private equity and retail turnaround groups, such as Sun Capital, Hilco and Gordon Brothers.
Large-format retailers, such as Macy's Inc and Kohl's Corp, are also potential suitors, he said in a note to clients, as are Canadian operators, such as Hudson's Bay Co , that may want to expand and fend off new rivals.
A Hudson's Bay spokeswoman said the company would not comment on speculation.
($1 = 1.0906 Canadian dollars)
(Additional reporting by Solarina Ho and Euan Rocha in Toronto; Editing by Savio D'Souza, Lisa Von Ahn, Jeffrey Hodgson and Eric Walsh)