The Twitter initial public offering culminated with the ringing of the New York Stock Exchange's opening bell Thursday, the social media site becoming a public company valued at more than $14 billion. But Twitter co-founder Jack Dorsey isn't done with Wall Street yet, as he's reportedly begun exploring an IPO for Square, the mobile payments startup he co-founded in 2009.

The mobile point-of-sale hardware and payments processor vendor has discussed a 2014 IPO with Goldman Sachs and Morgan Stanley, The Wall Street Journal reports.

Square is expected to process $30 billion in credit card transactions and generate sales of $1 billion in 2014, according to unnamed company sources cited by the newspaper's technology blog. The report adds that Square is projected to generate $550 million in sales off $20 billion in processing volume in 2013, resulting in net revenue of $110 million to $165 million after fees paid to credit card companies.

Representatives from Square, Goldman and Morgan Stanley did not comment on the WSJ story, and a Square representative did not respond to PaymentsSource's request for comment by deadline.

If Square is considering going public, the process is in its infancy, as the company has not hired an underwriting bank and the timing of the deal could change, the report says. Goldman Sachs CFO David Viniar joined Square's board last week, replacing Starbucks CEO Howard Schultz.

Since launching its Square Reader, which allows merchants to use smartphones and tablets to accept swiped card payments, the company has expanded its offerings to appeal to larger merchants with its "Business in a Box" product and its Square Stand iPad cradle, and has also added features designed for restaurants.

Meanwhile, the company has developed consumer-facing products including a mobile wallet and an online storefront called Square Market, as well as its Square Cash P2P payment system.

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