Visa Inc. may raise as much as $17 billion in what would be the biggest American initial public offering as the largest credit-card network tries to replicate the success of MasterCard Inc.

Visa plans to sell 406 million Class A shares for $37 to $42 each, the San Francisco-based company said in a regulatory filing yesterday. Banks have the option of selling an additional 40.6 million shares, pushing the size of the deal to $18.8 billion.

The IPO would eclipse AT&T Wireless Group’s $10.6 billion stock offering in 2000. Visa is pursuing its share sale as consumers turn from cash to credit cards and debit cards for a majority of their purchases. MasterCard has surged more than fivefold in New York trading since its IPO almost two years ago.

“People might argue that it’s growing faster than MasterCard in terms of transactions,” an analyst at Renaissance Capital in Greenwich, Conn., Paul Bard, said. Investors “might look to pay a slight premium to MasterCard.” The offering could leave Visa with a stock market value of more than $32 billion, which would be comparable to MasterCard’s current value of about $26 billion, Mr. Bard said. The pricing of Visa’s shares looks “very similar to where MasterCard is” trading, at about 27 times 2008 earnings, he said. The chief executive officer of Visa, Joseph Saunders, is pressing ahead with the sale amid a slump in the IPO market. Demand for initial public offerings has waned this year, with 100 companies raising $12 billion.