"The theory has always been the sum of the parts is worth considerably more than the whole," said analyst Dick Bove, vice president for equity research at Rafferty Capital Markets. "You might find a lot of investors who say that (if) they're going to break up these banks, they're more [valuable] in pieces than they are together, I'm going to buy them."

Bank stocks rallied, with investors taking a win-win view: Breaking up the big banks would open business opportunities for smaller institutions, while the large Wall Street firms would be worth more as separate entities than they are combined.

Major averages slipped as the news broke , then rebounded, while government bond yields hit their highs of the day.

In an interview Monday with Bloomberg News, Trump said he is "looking at that right now."

President Donald Trump is considering breaking up the nation's biggest banks, a vow he had made during the presidential campaign then seemed to put on the back burner.

Bank of America shares jumped 1.7 percent, a high for the session, while JPMorgan Chase was up 0.6 percent.

The SPDR S&P Bank exchange-traded fund was up 1.2 percent, also a high for the session.

Banking expert Christopher Whalen agrees with the sum-of-the-parts theory.

"You'd have more competition in the industry," said the head of Whalen Global Advisors. "If investors could buy a pure-play JPM and not have to own Chase, that's a much better stock. That's a stock that trades at 1.5 to 2 times book value instead of 1."

Whalen said spinning off Merrill Lynch from Bank of America also could prove beneficial. BofA bought Merrill during the financial crisis.

The industry breakup would come with the revival of a Glass-Steagall-type law, which separated commercial and investment banks but was repealed in 1999.

Trump's sentiments came the same day he met with leaders of the Independent Community Bankers of America, an advocacy group for small- and mid-market institutions.

Industry analyst Dick Bove believes that may not be a coincidence.

"He probably made a statement to them that they wanted to hear," Bove said. "In the last few weeks he has been heavily campaigning again, and I think this is just part of his campaign."

Whether anything will come of it legislatively is unclear.

"I just think he had a need to communicate, to connect again with community banks and say, 'Hey guys, we're on your side. We believe in you and maybe we should break up the big Wall Street banks,'" Bove added. "But I don't expect anything to come of it."

Bank stocks had been one of the biggest winners of the Trump trade, rallying strongly after his victory in the November presidential election. The sector rallied more than 25 percent in the immediate aftermath, but the bank ETF is down about 1.3 percent in 2017.

The Glass-Steagall repeal is sometimes blamed for the financial crisis that peaked in 2008. However, many of the big institutions at the center of the crisis were not banking behemoths but rather investment banks or, in the case of American International Group, an insurer.

Still, the Republican platform last year carried language calling for a reinstatement of the law.

"There's some people that want to go back to the old system, right? So we're going to look at that," Trump said in the interview.

Watch: Don't adjust portfolio based on Trump's bank comments