Davis campaign spokesman Hector Nieto would not confirm that Davis is running.
"As senator, Davis told grass-roots supporters last week via email, she's made a decision and she looks forward to making her decision public on Oct. 3," Nieto said.
Republican Attorney General Greg Abbott announced his candidacy this summer and is the early favorite to succeed Gov. Rick Perry, who is not seeking re-election after 14 years in office.
No other Democrat has expressed interest in running for governor in Texas, where a Democrat hasn't won a statewide office in 20 years. Experts say Davis would need to raise $40 million to mount a serious campaign. Abbott has raised more than $20 million.
For months, Democrats have urged Davis, 50, to run.
Davis' progressive politics and charisma on the campaign trail have long made her popular among Texas Democrats. But it was her filibuster in the Texas Capitol on June 25 defending women's right to an abortion that won her fame across the U.S. The filibuster helped temporarily block new statewide abortion restrictions. She has attended fundraisers in New York, Washington and San Francisco.
The last Democrat elected governor was the late Ann Richards in 1990. Richards was defeated by George W. Bush in 1994 and Republicans have held the office ever since. The GOP has also held every statewide office in Texas since 1998 and the controlled the Legislature since 2003.
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