Square has been in talks with several rivals for a possible sale as the mobile payments startup looks to stem widening losses and dwindling cash, The Wall Street Journal reported, citing people familiar with the matter.
The company spoke to Google earlier this year about a possible sale, the Journal reported, adding that it wasn't clear whether the talks are continuing.
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Square, founded in 2009 by Jack Dorsey, co-creator of Twitter, will likely fetch billions of dollars in a sale. Square insiders sold shares earlier this year on the secondary market, valuing the company at roughly $5.2 billion, the Journal said.
The company recorded a loss of about $100 million in 2013, the Journal said, adding that the startup has consumed more than half of the roughly $340 million it raised from at least four rounds of equity financing since 2009.
Square makes credit card readers that slot into smartphones such as Apple's iPhone.
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Square also had informal discussions about a deal with Apple and eBay's PayPal in the past, but those conversations never developed into serious talks, the Journal said.
A spokesman for Square told the Journal that the company never had acquisition talks with Google. The report also quoted a PayPal spokesman as saying that the company did not have acquisition talks with Square.
"We are not, nor have we ever been in acquisition talks with Google, and while we appreciate that Square may be an attractive target for some companies, we have never seriously considered selling to anyone or been in any talks to do so," a Square spokesperson told CNBC Monday.
Square, Google, Apple and eBay were not immediately available for comment outside regular U.S. business hours.
Square held discussions with banks such as Goldman Sachs and Morgan Stanley in November about a possible initial public offering in 2014.
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However, the company's planned IPO has been postponed "indefinitely," according to media reports last month.
—By Reuters. CNBC contributed to this report.