“It will ultimately be a family decision,” Ms Harris, who represents the state of California, told MSNBC during an event in San Francisco.
“And over the holiday, I will make that decision with my family.”
Ms Harris, 54, was elected to the Senate in 2016.
She ranked fifth in a November poll of Democratic voters’ preferred nominee to take on President Donald Trump’s re-election bid, Politico news reported on Sunday.
Ms Harris has sent $25,000 to the Democratic parties in four early nominating states: Iowa, South Carolina, Nevada and New Hampshire.
In October, she visited Iowa, South Carolina and Wisconsin to campaign for Democratic candidates ahead of the midterm elections.