JPMorgan Chase & Company is in talks to acquire Bank of New York’s retail-banking business, according to a person familiar with the matter.

A deal, if it comes to fruition, could take the form of an asset swap. For example, Bank of New York could exchange its retail-banking arm for part of JPMorgan’s worldwide securities services unit – perhaps its trust division. Such an arrangement could complement both companies’ existing business lines while avoiding the hefty tax implications of a cash deal, according to bankers not involved in the negotiations.

The discussions haven’t reached a final stage, according to the person familiar with the matter. Spokesmen for both banks declined to comment.

The talks were first reported yesterday morning by CNBC, which said a deal could involve up to 300 Bank of New York branches and could fetch as much as $4 billion.

For JPMorgan, which already is the biggest bank in the lucrative and fiercely competitive New York area, a deal with Bank of New York would help it expand its lead over rivals such as Citigroup and Bank of America. Meanwhile, Bank of New York would shed an underperforming unit at a time when other New York banks have attracted high prices in recent takeovers, allowing it to better focus on its main securities-processing business.

A Prudential Equity Group analyst, Michael Mayo, wrote last week that a spin-off would be well timed and would let Bank of New York’s shares trade at a higher multiple.

“The performance of the Bank of New York’s retail bank has lagged, the stock value of pure-plays has increased, and Bank of New York stock has lagged,” Mr. Mayo wrote. “We sense that the time is right for this move.”

Bank of New York shares jumped 4.2% to $35.86. JPMorgan shares recently traded for $41.34 each, down 0.8%.

Bank of New York – the nation’s oldest bank, founded by Alexander Hamilton in 1784 – has long been rumored to be mulling a sale or spinoff of its 342-branch retail network. That speculation escalated recently after Capital One Financial Corporation agreed to pay a rich premium to acquire New York-area banker North Fork Bancorp.

Bank of New York executives haven’t done much to damp those expectations. At a conference last month, the president of Bank of New York, Gerald Hassell, nearly made it through an investor presentation without mentioning the retail business. When an analyst asked him about the unit’s future, he said: “It’s a business that we continue to look at to make sure [it is] returning what we expect of them.”

Almost all of Bank of New York’s branches are in the New York area. JPMorgan, by comparison, has more than 2,600 branches in 17 states. But JPMorgan underinvested in its branches earlier in the decade, allowing rivals like Bank of America, Commerce Bancorp, and HSBC Holdings’s American unit to chip away at its dominant position in New York.

Chief Executive Jamie Dimon, who boasts that JPMorgan New York’s “hometown bank,” has vowed to protect the company’s share of the metropolitan area’s deposit market, which currently stands around 24%.