The market is still coming to terms with the possibility of two interest rate hikes this year, but former Wells Fargo Chairman and CEO Richard Kovacevich is not discounting the possibility of a third by the end of 2016.
He said the Federal Reserve should raise interest rates in June to determine whether the market will bear further rate hikes later this year.
"It gives them the option then, if they want to and it's supported by the data, to move in September and even December," he told CNBC's "Squawk Box" on Thursday.
"I think they should move as early as possible so they have more time to wait to see the reaction to it before they decide to do September or December," he said.
The market had not been expecting a summer rate hike until minutes from the Fed's April meeting showed policymakers were likely to raise rates if data pointed to stronger second-quarter growth, as well as continued labor market improvement and progress toward the Fed's 2 percent inflation target.
The Fed has kept rates close to zero for seven years, sending a message at policy meetings that the economy is not strong enough to support higher rates, Kovacevich said.
The business community has taken that message to heart, but the Fed's economic forecasts are wrong as often as they are right, he added.