The encouragement, which was relayed to The Texas Tribune by two Republican sources familiar with the correspondence, came around the same time that McCaul, an Austin Republican, emerged as a top potential challenger to Cruz's re-election efforts, amid an outcry among many grassroots conservatives over Cruz's decision not to endorse presidential nominee Donald Trump at the Republican National Convention.
A Perry spokesman wouldn't say whether the former governor made such overtures to McCaul, instead praising the six-term member of Congress.
"Rick Perry holds Michael McCaul in the highest esteem," Perry spokesman Stan Gerdes wrote in an email.
A spokesman for McCaul declined to comment.
The rumblings about a McCaul Senate bid began in July, when Cruz's RNC speech telling Americans to vote their "conscience" drew boos from the arena floor. His Republican detractors in Texas — both donors and operatives — sensed an opportunity, and began to consider backing a primary rival.
McCaul is the current vessel for that effort. He, or any serious GOP challenger, will likely have financial backing from some deep-pocketed Texas donors unhappy with Cruz. Many in this movement are searching feverishly for a candidate if McCaul opts out.
Last week, McCaul publicly criticized Cruz, but declined to say whether he would vie to unseat him.
"I think he's spent a lot of time since Day One running for president," McCaul said in an interview with The Texas Tribune in Austin on Tuesday. "I think we deserve somebody in the Senate who is going to be representing the interests of the state of Texas."
A spokesperson for Cruz declined to comment. The senator has previously said he's not taking his re-election for granted, but he has not directly commented on a potential McCaul challenge.
"I think every elected official should approach the job every day working hard to earn the votes of Texans," Cruz said in September at the Texas Tribune Festival. "There's an old joke — there's two ways to run: scared or unopposed."
Even amid Perry’s encouragement, it remains unclear if McCaul will follow through on a run. If he bows out, attention on a potential Cruz challenger could shift to Perry.
While the former governor was a loyal surrogate for Cruz during this year's primaries — at least, once Perry was out of the presidential race — he was not always a fan. Perry was an ardent backer of Lt. Gov. David Dewhurst's failed bid to win the open U.S. Senate seat that Cruz won. In his own 2016 campaign for president, Perry frequently alluded to Cruz as unready for the White House. Ultimately, Perry endorsed Cruz's presidential run.
Within the anti-Cruz contingent, Perry is perceived as one of the few GOP players with the statewide stature and name identification to launch a serious challenge to Cruz.
“My preference of what’s next for Rick Perry is not to be in the United States Senate,” Perry said.
At the same time, Perry has proven to be restless in his retirement.
He was active on the presidential campaign trail for Cruz, an omnipresent politician at the Republican National Convention in Cleveland and most recently, a contestant on “Dancing with the Stars.”