REUTERS/Mark Kauzlarich
Sen. Ted Cruz (R-Texas).
According to the report, Cruz raised doubts about Trump at a private Manhattan fundraiser on Wednesday.
"Both of them I like and respect," Cruz reportedly said of Trump and Ben Carson, another Republican presidential candidate.
"I don't believe either one of them is going to be our president," he added.
The Times' Maggie Haberman and Matt Flegenheimer, citing attendees, wrote that Trump then brought up last week's mass shooting in San Bernardino, California, and last month's terror attack in Paris, France.
"You look at Paris, you look at San Bernardino, it's given a seriousness to this race, that people are looking for: Who is prepared to be a commander in chief? Who understands the threats we face?" Cruz was quoted asking. "Who am I comfortable having their finger on the button? Now that's a question of strength, but it's also a question of judgment. And I think that is a question that is a challenging question for both of them."
The report is notable as Cruz has been one of the few Republican presidential contenders to consistently refuse to criticize Trump, the party's front-runner who has repeatedly ignited national firestorms with his provocative statements and policy proposals.
In turn, Cruz has been the only notable Republican candidate whom Trump has refused to insult as his rallies. However, Trump recently started predicting that Cruz, who has started to surge in the polls, would eventually attack him.
Most recently, Trump drew intense backlash this week from both Republicans and Democrats with his proposal to temporarily bar almost all Muslims from entering the US, including both immigrants and tourists. Some of Trump's rivals have used terms like "ridiculous" and "unhinged" to describe the idea, but Cruz has only publicly said that he disagrees with the plan.
Reached for comment, Cruz spokesman Rick Tyler simply told The Times: "Judgment is a question for all candidates for president of the United States. That is the point Cruz was making."