Who is Ted Cruz vetting as potential running mate?

Ted Cruz's presidential campaign is vetting former presidential contender and former Hewlett-Packard CEO Carly Fiorina as a potential running mate, a source close to Fiorina confirmed to CBS News on Monday.

The Texas senator's campaign manager, Jeff Roe, tweeted Monday that they had narrowed a list of vice presidential candidates.

We have narrowed our VP candidates to a short list and are going thru the normal processes associated with picking a running mate.#CruzCrew

— Jeff Roe (@jeffroe) April 25, 2016

Speaking to reporters Monday afternoon, Cruz wouldn't openly acknowledge Fiorina was being vetted.

"We have acknowledged some time ago that we have begun a vice presidential search process. Any responsible candidate just a couple of months out from the convention would begin that process," he said. "We've begun examining both a long list and now a shorter list that has been called. And that naturally includes a vetting process. At this point, no decisions have been made in terms of who a nominee would be. Or what the timing would be of the announcement."

Although the nominee is not yet settled, candidates who haven't started their selection process should get moving, a panel made up of some of the nation's top presidential campaign advisers and operatives suggest. In a report published Friday by the Bipartisan Policy Center, the group, co-chaired by former Obama campaign General Counsel Bob Bauer and by a top McCain campaign adviser, Charlie Black (who is now advising John Kasich), recommended that the candidates should begin their selection process at least eight weeks before the convention. The window for this is shorter in 2016, given the fact that the nominating conventions will take place in July, instead of August.

Fiorina, who dropped out of the race in February, endorsed Cruz last month. Cruz has decided to team up with John Kasich to try and block Donald Trump from receiving the GOP nomination.

According to CBS News' latest count, Trump leads with 844 delegates, Cruz has 555 and Kasich has 147.

CBS News' Steve Chaggaris and Ann Jacob contributed to this report.