Inflation is cooling, but the Fed is going to remain aggressive until it falls closer to its target, former Treasury Secretary Jacob Lew says

• The Federal Reserve will remain aggressive despite cooling inflation, according to Jacob Lew.
• The former Treasury Secretary told CNBC on Tuesday that inflation has yet to fall to a "safe zone."

Don't expect the Federal Reserve to pivot from tightening monetary on signs of cooling inflation.

That's according to former Treasury Secretary Jacob Lew, who told CNBC's Squawk Box on Tuesday that inflation has yet to reach a "safe zone," and "that's going to take a long time."

"I think all the market speculation about 'is the Fed going to move quickly' to me is premature," Lew said. "I don't think the Fed is going to change its course."

Lew's comments preceded the November consumer price index report, which showed inflation further cooling to 7.1% last month, below a consensus expectation of 7.3%.

"It's a tough balance between making sure you deal with inflation but that you don't trigger a deeper recession and more unemployment than you need," Lew said.

But whether or not the reading came in on Tuesday slightly lower or higher would ultimately do little to sway the Fed, Lew added, and he expects the central bank to "hang tough."

Still, Lew was optimistic that inflation is heading in an encouraging downward direction, and thinks "we're not going to stay at these very high levels."