Gallegos, a Houston Democrat, died of liver disease on Oct. 16. It was too late to remove his name from the Nov. 6 general election ballot and he was posthumously elected to another term.
Candidates for the District 6 special election must file by Dec. 27. Early voting will run from Jan.9-22.
State Rep. Carol Alvarado, a Houston Democrat, has said she will run for the Senate seat.