Dow futures trimmed earlier gains as U.S. oil prices turned lower after a five-session winning streak.
Despite market expectations for up to two cuts this year, Bostic said the Fed should stay put.
Stocks fell on Thursday, with most of the losses coming in a sudden, rapid move midday.
U.S. stock futures were indicating a higher Wall Street open, after the Dow eked out another record high close Monday.
"We're gonna take this meeting by meeting. We're not on a preset course," Clarida told CNBC.
Japanese-style interest rate caps are drawing interest from global central bankers worried about a downturn, including U.S. Federal Reserve officials.
Federal Reserve Vice Chairman Richard Clarida said Tuesday that he would take the inverted yield curve "seriously" if it "persists for some time."
He said he will be watching current conditions, in particular the trade war and the inverted yield curve in the bond market, for clues about where the Fed should go next.
Stocks fall sharply after China decides to raise tariffs on $60 billion worth of U.S. goods.
The dollar slipped against a basket of currencies on Friday as traders focused on the weaker aspects in the April U.S. payrolls report, brushing aside stronger-than-forecast hiring and a drop in the jobless rate to the lowest in more than 49 years.