Cornyn's spokesman Kevin Mclaughlin said the senator is not trying to block her confirmation, but is seeking more debate on the donation issue.
Jim Manley, spokesman for Senate Majority Harry Reid, D-Nev., said that if a voice vote is blocked there will be a roll call vote Wednesday. He predicted that "she will receive overwhelming bipartisan support at that time."
The Senate does plan to confirm several of President-elect Barack Obama's Cabinet by unanimous vote later Tuesday.
Several Republicans raised questions at Clinton's confirmation hearing about possible conflicts of interest from Bill Clinton's fundraising work and his acceptance of large donations from foreign countries and companies.
Sen. Richard Lugar of Indiana, top Republican on the Foreign Relations Committee, urged Clinton to improve transparency in her husband's fundraising activities. He said the former president's foundation should stop taking foreign contributions while Clinton serves as secretary of state. McLaughlin said Cornyn has asked Clinton to take similar steps.
In her testimony, Clinton said the foundation would provide a clearer picture of its annual donations.