Yellen may have just gotten her excuse: Ex-Fed Gov. Lindsey

The spiraling Greek debt crisis might just be the cover the U.S. central bank, led by Janet Yellen, has been looking for to put off increasing interest rates, former Fed Gov. Larry Lindsey said Tuesday.

"They are going to use this as another reason to delay," argued Lindsey, also director of the National Economic Council for President George W. Bush. "The problem is all the [rate hike] delays haven't solved anything."

Read MoreThe latest on the Greece debt crisis

The CEO of economic advisor The Lindsey Group warned on CNBC's "Squawk Box" that U.S. debt and capital market distortions keep building. "Eventually, the Fed will find itself way behind the curve. And that is going to be a very disturbing event for the markets and the economy."

Southern Co.'s chairman and CEO, Tom Fanning, also chair of the Atlanta Fed's board of directors, told CNBC he agrees with Lindsey that Greek uncertainty could delay the central bank's first rate hike since 2006.

"Everybody is fixated on when's liftoff. Is it going to be September, December or even 2016? But I think the bigger question is the forward trajectory," he said, "and how regular, predictable and sustainable will Fed actions be."

Read More Others say Greece is just a sideshow for the Fed

The debate on Wall Street has centered on whether the initial move would come at the Fed's September or December meeting or even later, because both gatherings have a Yellen news conference scheduled.

A handful of Fed policymakers in their forecasts after the June meeting revealed they expected two rate increases this year.

Using overnight index swaps, RBS calculates a 30 percent chance of a 25-basis-point increase in September.

There was some movement away from September to later in the year when Greece started boiling over. Odds had been at more than 60 percent in early June for a September move.

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—CNBC's Patti Domm contributed to this story.

Clarification: This story has been updated to use RBS' calculations of a possible Fed move.