Sen. Bob Corker of Tennessee said in an interview Tuesday on MSNBC that Clinton probably will testify the morning of Jan. 22.
The State Department said the date hasn't been finalized and there was no official word from the committee.
Clinton had been scheduled to testify last month but fell during an illness, suffered a concussion and was hospitalized for a blood clot.
Clinton returned to work Monday. She had promised to appear before the Senate and House foreign affairs panels before stepping down from her job. Obama has nominated Sen. John Kerry to replace her.
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