O'Rourke campaign manager Jody Casey made the proposal in a letter last week to Cruz's senior staff, adding that the debates should have "media reach to all twenty markets in the state."
"I would like to begin direct coordination of the debates with your campaign team between now and May 10th," Casey wrote to Cruz advisers Bryan English and Eric Hollander in the April 24 letter. “Please advise my best point of contact on the Cruz campaign team."
Cruz previously suggested he is open to debating O'Rourke. Cruz's campaign said in response to the letter that it was exploring its options.
"Sen. Cruz has said he's looking forward to debates," Cruz spokeswoman Catherine Frazier said in a statement. "We are considering all possibilities in front of us and will be working with potential hosts and the O'Rourke campaign to determine the best platforms available so that Texans from all corners of the state can hear from the candidates directly about their views for Texas' future."
Regardless of what the campaigns ultimately agree to, debates in Spanish between the candidates seem unlikely. While O'Rourke is fluent in the language, Cruz is not known as a proficient speaker.
After a campaign event Tuesday afternoon in San Antonio, Cruz admitted to reporters that his Spanish "remains lousy" before offering a sentence in the language: "I understand almost everything, but I can't speak like I want to."
Cruz, whose father came to America from Cuba, chalked up his shoddy Spanish skills to "the curse of the second-generation immigrant," adding that he suspects many in the Hispanic community can relate.
"A debate in Spanish would not be very good because my Spanish isn’t good enough, but I look forward to debating Congressman O’Rourke," Cruz said.
Cruz has professed little resistance to sparring with O'Rourke so far. Asked in March if he would debate O'Rourke, Cruz told reporters he is "sure we'll see a debate in this race." Cruz noted that he debated U.S. Sen. Bernie Sanders, I-Vt., multiple times on national TV last year before adding, "I am not remotely afraid to debate left-wing liberal socialists."
During a conference call with supporters Thursday, O'Rourke alluded to the letter while fielding a question about whether there will be a debate between him and Cruz.
"We certainly want a debate," O'Rourke said, adding that his campaign is working to "make sure that we give every voter in Texas the opportunity to know the difference between the two candidates, their track record of service, what they hope to achieve for the state of Texas and the way in which they are campaigning."
O'Rourke suggested he was undeterred by Cruz's past as a college debate champion and a lawyer who has argued before the U.S. Supreme Court nine times.
"While I know that Cruz is a master debater, a very skilled politician, a very shrewd person ... I would love the opportunity to talk about what all of us have been doing together over the course of the campaign and what we want to achieve for Texas," O'Rourke told supporters. "I’m very much looking forward to it."