Story highlights Carly Fiorina and a handful of other possible vice presidents for Ted Cruz have agreed to submit tax returns

Cruz's campaign has not ruled out naming a vice-presidential candidate before he wins the GOP nomination.

Washington (CNN) Carly Fiorina and a handful of other possible vice presidents for Ted Cruz are submitting tax returns, said a source familiar with the process Tuesday, another step in the Texas senator's vetting process.

Cruz's campaign has not ruled out naming a vice presidential candidate before he wins the GOP nomination. And Fiorina, a popular Cruz surrogate and a former presidential candidate, quickly emerged this week as someone the Cruz campaign confirmed it was vetting.

Fiorina's team said Monday that she was being vetted and going through the "standard stuff," but a Fiorina spokesman on Tuesday did not immediately respond to a request for comment.

Earlier on Tuesday, however, Cruz distanced himself from another possible vice president: Ohio Gov. John Kasich, with whom Cruz has struck an unusual pact in several of the remaining states on the calendar.

"I think that is very, very premature. I respect John Kasich, he is a good and capable man, but I think at this point we've made a decision about allocation of resources," Cruz said to Indiana radio host Tony Katz, pushing back on the idea that the alliance could be a precursor to a ticket. That's an idea that has been pushed by at least one major Cruz donor

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