Republican Carly Fiorina, former Hewlett-Packard CEO, announced Tuesday she has registered “Carly for California” with the IRS to begin the formal process of exploring a 2010 bid to challenge Democratic Sen. Barbara Boxer of Calfornia.

“I have received a great deal of enouragement to make a run for the Senate in 2010 from people across the political spectrum… today’s filing with the IRS is a logical next step in the process of evaluating running for this office,” Fiorina said in a statement.

The registration would allow Fiorina to form a 527 group to begin fundraising.