Senator Ben Cardin said he was not persuaded to support Tillerson's nomination even after the former Exxon Mobil chief executive spent an hours-long hearing earlier this month seeking to assure lawmakers that he was fit for the job.
Despite opposition from Democrats, Tillerson is expected to win confirmation, Reuters reported.
Republican Senators John McCain and Lindsey Graham said in a statement on Sunday they would vote to approve Tillerson despite their concerns over his relationship with Putin.
Republican Senator Marco Rubio, who grilled Tillerson during the hearing, has not said yet how he will vote.