WASHINGTON—A Senate committee is on track to vote Monday against endorsing the nomination of CIA Director Mike Pompeo to be secretary of state, which would mark an unusual rebuke to a central member of President Donald Trump’s foreign policy team.

The Senate Foreign Relations Committee is scheduled to vote on Mr. Pompeo’s nomination on Monday evening. All of the panel’s Democrats have said they would oppose the former congressman’s nomination, and they have been joined by one Republican, Sen. Rand Paul of Kentucky.

That...