The Federal Reserve should keep the option of another interest-rate increase on the table, depending on inflation progress, but the weaker-than-expected October jobs report is welcome evidence that the labor market is normalizing, Richmond Fed President Thomas Barkin said Friday.

Slowing hiring last month follows anecdotal reports from business contacts that labor demand is cooling, particularly for professionals, he said in a CNBC interview. "What we saw today was data that showed gradual lessening of the job market, and I think that's what those who would like to not see another rate hike would like to see," he said. Whether he would support another rate hike, Barkin said: "I won't prejudge that. I value the optionality." (See: MNI INTERVIEW: 2024 Fed Hikes Possible On Fiscal Boost-Kaplan)

He noted lower-income consumers are "reprioritizing" how and where they spend while middle-income consumers are trading down. Wealthier consumers are still spending extravagantly on services, Barkin said. "I still think there's a good chance of what we're seeing on the consumer side is a normal economy, a solid economy, not a frothy economy."