Fiorina is expected to formally announced her Republican campaign online and hold a conference call for the national press, according to the Journal.
She would join U.S. Senators Ted Cruz, Marco Rubio and Rand Paul as declared Republican candidates.
One of Fiorina's biggest challenges may be raising the money she'll need to stay in the race long enough to build up more name recognition. She contributed $5 million of her own money to her Senate campaign, but left behind more than $500,000 of debt.
Fiorina is back in New Hampshire this week, joining a multitude of potential GOP presidential candidates at a two-day forum that could be an early test of who has breakout potential in the state that holds the nation's first primary.
Fiorina says she doesn't want to run based on her sex, but rather to focus on another factor that makes her an outlier in the Republican field: the fact that nearly her entire career has been in business, not the political arena. She was one of the country's highest-ranking female executives during her nearly six years as chief executive at Hewlett-Packard, but was forced out of the company in 2005.
Fiorina ran for the U.S. Senate in California in 2010 but was easily defeated by incumbent Democrat Barbara Boxer. She was an adviser to Sen. John McCain's unsuccessful 2008 presidential campaign.
--AP contributed to this report.