Former Federal Reserve Chairman Alan Greenspan warned Tuesday that inflation is going to pose a larger threat to the U.S. economy as budget deficits continue to rise.

"Right now, there's no real inflation at play. But if we go further than we are currently, inflation is inevitably going to rise," the 93-year-old ex-central bank chief said on CNBC's "Squawk on the Street."

As things stand, the U.S. inflation rate for years has held below the 2% level that the Fed considers healthy for a growing economy, at least gauged by the central bank's preferred measure.

That has come even though the 3.5% unemployment rate is the lowest it's been in 50 years. Fed economists closely watch what is known as the Phillips curve, which traditionally has indicated that lower employment will drive higher wages and push inflation gauges up simultaneously.

The U.S. ran a fiscal deficit in 2019 that just missed $1 trillion. As those excess dollars float through the system, that historically has driven inflation higher.