A monthlong, double-digit slide in the shares of Firstar Corp. and its merger partner, U.S. Bancorp, is casting doubt on the planned combination and has even dredged up rumors that the latter passed up a lucrative cash takeover bid earlier this year.

Shares of the two companies have skidded virtually in lockstep, down nearly 13% since the deal was announced Oct. 4. The pain may be worse for U.S. Bancorp shareholders, however. Their stock has dropped 36% since last year after a string of disappointing profit reports and the resignations of key senior executives.

In interviews with investors and analysts last week, a number of people still expressed support for the deal. There was, however, a fair amount of grumbling.

Announcing their deal, executives at the two companies vowed that they would stay out of the merger game as they worked through the details of their integration and got the combined company’s revenue-generating engines up to full speed.

As investors and analysts see it, however, that was what Milwaukee-based Firstar promised after its last deal, the purchase of St. Louis-based Mercantile Bancorp. Just weeks before the U.S. Bancorp deal was announced, Firstar executives were telling investors they were finished with big transactions until they could prove themselves to Wall Street. Those statements came after a two-year buying spree that had tripled Firstar’s size and geographic reach.

By jumping into another big deal just months after completing the Mercantile integration, investors and analysts said, Firstar harmed its credibility. “The deal certainly wasn’t received well — the marketplace is voting that way,” said Steven Schroll, vice president and senior securities analyst at American Express Financial Advisors, a fund management subsidiary of American Express Co.

Management “had said, ‘No big deals for a while’ and then they did a big deal,” said Steven Wharton, an analyst at Loomis Sayles & Co.

A U.S. Bancorp spokesman had no comment.

Doubts over Firstar’s ability to take on another big integration heightened at mid-month when it reported third-quarter earnings. Though the company matched analysts’ consensus profit estimate, investors noting the company’s sluggish revenue growth pushed down its shares by 14%, to $19.625, in the two days after the report.

The decline in Firstar has sparked some speculation that U.S. Bancorp could have sold itself to another company for more money and, more importantly, for cash. Firstar’s offer calls for an exchange of 1.265 of its shares for each share of U.S. Bancorp. At the time it was announced, the deal price was roughly $21 billion, but it would now be closer to $17 billion.

Investors said rumors have resurfaced that a large European banking company had made such a cash offer last summer and might step up again. The preeminent rumor in months past was that ABN Amro, the Dutch financial services giant that owns LaSalle Bank in Chicago and European American Bank in New York, had expressed interest in expanding its retail presence in the Midwest and would be interested in buying Minneapolis-based U.S. Bancorp.

“There’s a legitimate argument that a foreign buyer would make a better deal in the short term,” said Stephen Berman, an analyst in the financial services group of Stein Roe & Farnham Inc.

“I’m sure there were other interested parties, but if they were so interested, why didn’t they come forward?” said Michael J. Stead, portfolio manager in the SIFE Trust Fund, which owns stakes in both Firstar and U.S. Bancorp.

Several investors said they still like the deal because it would create a valuable banking franchise, even if such a result is not apparent for at least a year.

“It has the potential to become a top-tier regional bank with double-digit revenue growth,” said Mr. Berman, whose firm bought Firstar shares when the deal was announced.

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