The Fed taper is not only inevitable but already priced into the stock and bond markets, one of Wall Street's most famous investors suggested Monday.
But the consensus on Wall Street is that the Fed probably will begin dialing back its $85 billion in monthly bond purchases by the end of the first quarter or in the second quarter, he said.
"If the inflation rate is too low to suit the Fed and the unemployment rate is too high.. that tapering will begin. It's gotta begin sometime," Bogle said.
Last week on "Closing Bell," Pimco's Bill Gross said that Fed Vice Chair Yellen, who will soon succeed Fed Chairman Ben Bernanke, will likely be "focused on exiting QE" in the new year. Though Gross runs the world's largest bond fund, he praised Bogle's outperformance in index funds.
(Read more: 2014 will center on the Fed, Gross says)
Indexing is a type of mutual fund built with a portfolio of stocks meant to track the components of a market index, such as the S&P 500. With broad market exposure, it is said to typically outperform actively managed mutual funds.
Bogle said he's content with indexing's performance in 2013 and will continue to execute this strategy in the new year.