WASHINGTON—A group of Senate Democrats have privately voiced their opposition to President Biden’s nomination of Saule Omarova to become a top banking regulator, likely scuttling the academic’s chances of confirmation.

Sens. Jon Tester of Montana, Kyrsten Sinema of Arizona and Mark Warner of Virginia—who are centrist Democrats—conveyed their opposition to Senate Banking Committee Chairman Sherrod Brown (D., Ohio) on a Wednesday telephone call, according to a person familiar with the discussion.