Story highlights Ted Cruz's campaign is "narrowing" its list of potential vice-presidential choices

One Cruz aide said that Carly Fiorina was on the list of possible candidates

Washington (CNN) Ted Cruz's campaign is vetting a list of potential vice-presidential choices including Carly Fiorina, an indication that the campaign could choose a running mate while he continues to battle for the GOP nomination.

The Texas senator is considering naming Fiorina, a prominent Cruz surrogate and a former GOP White House rival, as his running mate, a Cruz campaign adviser confirmed Monday. Presumptive nominees typically vet many possible vice presidents, asking them for extensive financial documents and thoroughly investigating their backgrounds.

"He is vetting a number of solid candidates, and certainly Ms. Fiorina is absolutely one of them," Chad Sweet, Cruz's campaign chairperson, told CNN's Jake Tapper on "The Lead." "She's one of the most talented business leaders of modern times."

Fiorina aide Sarah Isgur Flores also confirmed that the former Hewlett-Packard CEO was being vetted for a possible pick on a Cruz ticket.

Cruz and top Cruz aides Monday sought to end a day of news reports about Cruz's veepstakes, downplaying any vetting as a normal part a fall campaign plan. Cruz himself preached prudence.

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