Privately held BJ's Wholesale Club, the members-only warehouse retailer, is preparing for a sale and e-commerce giant Amazon (AMZN) is reportedly eyeing it, according to the New York Post.

After ditching plans to take BJ's public amid the growing decline in the retail industry, the company's private equity parents, CVC Capital Partners and Leonard Green & Partners, are pushing the company to sell itself. BJ's could be worth around $4 billion, sources told the Post.

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BJ's was taken private by CVC and Leonard Green in 2011 in a $2.8 billion buyout. That year, Walmart (WMT) had also made a play for BJ's, but was unsuccessful.

The interested buyers this time around include private equity firms KKR, Bain Capital, TPG Capital and Blackstone Group as well as Amazon. Walmart is not going to make a second attempt at a BJ's takeover, according to the Post.

"As a matter of policy, BJ's Wholesale Club does not comment on rumors and speculation," BJ's spokesman Kirk Saville said in an email.

Amazon did not return a request for comment.

Here are three reasons why Amazon should eat up BJ's.

Amazon needs a bricks-and-mortar presence.

Unarguably the number one benefit for Amazon in this potential deal would be the warehouses the e-commerce company would instantly gain. BJ's chain of 213 clubs in 15 states would give Amazon the edge it needs to continue to dominate the retail sector.

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As Amazon rival Walmart ramps up its shipping offerings, adding pickup discounts and free two-day shipping, it is becoming more and more apparent that Amazon needs to grow a store footprint. In a recent interview with TheStreet, Marc Lore, president and CEO of Walmart eCommerce U.S., said Walmart is even testing same-day home shipping. As Barclays' Karen Short pointed out in an interview, Amazon will have a tough time implementing same-day home shipping across the U.S. without obtaining more distribution centers.

A BJ's takeover would boost Amazon's grocery business.

The additional bricks-and-mortar space Amazon would gain in the takeover would specifically benefit its emerging grocery service. To give AmazonFresh the boost it needs to compete with Walmart's grocery business, it needs more delivery hubs. Amazon recently launched a service for its Prime members that delivers groceries right to their cars, but it's only available in two Seattle locations - as the company does not have the store presence to expand on the service significantly.

BJ's has something else Amazon could use.

BJ's is strong in one area of retail Amazon is still trying to enter with force - appliances and furniture. Last month, the New York Times revealed that Amazon was considering opening appliances and furniture stores - a move that TheStreet pointed out could be yet another deadly attack on traditional retailers such as Best Buy (BBY) and Sears (SHLD) . The New York Post said this area of the retail sector is one Amazon is really trying to boost and hopes BJ's would drive that.

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