Wharton School finance professor Jeremy Siegel warns that the seemingly endless bull-run market on Wall Street could be charging straight into a brick wall.

"It's possible we could have a little bubble like we had in January," he told CNBC. He thinks stocks could continue on a "sharp upswing that could end like what happened in January, but we're not there yet."

Shortly after January all-time highs, the Dow plummeted, and then bottomed out on March 23, before heading higher in fits and starts, CNBC.com explained.

Siegel also said the market could be "in the very early stage of another short-term bull run here."

Meanwhile, the bulls have regained control on the American equity market, Bloomberg reported.

The S&P 500 Index capped a second weekly advance, ending the five days less than two points away from its all-time high. Investors plowed $38 billion into U.S. stock exchange-traded funds through Thursday, on pace for the best weekly inflow on record. Some $10.9 billion alone was poured into the biggest ETF that tracks the equity benchmark. Investors put $14.5 billion into U.S. equity funds in the week ending Sept. 19, according to EPFR Global data, the most since March.

Part of the surge in inflows is due to the revision to the Global Industry Classification Standard. The rally in U.S. equities has defied a chorus of calls for caution as investors looked past escalating tension over trade and a spike in 10-year Treasury yields to levels that roiled markets earlier this year. Not even the near-certainty that the Federal Reserve will lift benchmark rates next week slowed an advance that has the S&P 500 on pace for its best quarter since the heady days of 2013.

“If the economy is truly doing well, investors are willing to be in equities despite higher interest rates,” Patrick Palfrey, equity strategist at Credit Suisse Group AG, said by phone. “We don’t see the market euphoria seen in late January. The stocks are rising for the right reason.”