The Oscar-winner, who has publicly flirted with running for governor in the Lone Star state, avoided questions as he visited Capitol Hill on Monday, the same day he penned an op-ed column calling for stricter gun control in the US.
Senator John Cornyn, a Republican from Texas, is part of a bipartisan group meeting on possible gun legislation following the shootings in Buffalo, which killed 10, and Uvalde, where 19 students and two teachers were murdered.
Mr Cornyn told reporters that he had spoken to McConaughey on the phone and “may see him as a constituent”.
“I talked to him on the phone, he is a constituent of mine. And, you know, he wrote an op-ed piece in The Austin American-Statesman, and certainly, his voice is important but everybody’s voice is important in trying to figure out where the consensus lies for bi-partisan legislation,” he said.
Asked if he had met the actor in person, he said: “Not yet. I may see him as a constituent, he is a Texan after all.”
In his op-ed, McConaughey called for background checks, age minimums for gun ownership and mandatory waiting periods before the purchase of assault rifles as measures that could effectively diminish incidences of mass shootings in America. He also wrote with urgency about the need for more resources dedicated to mental health care.
Austin-based McConaughey returned to his hometown, where his mother had worked as a school teacher, three days after the mass shooting that left 19 children and two adults dead on 24 May.
Salvador Ramos, 18, had opened fire at the Robb Elementary School with a handgun and an AR-15 assault rifle, according to officials.
Writing in the Austin American-Statesman, McConaughey described his personal motivations for weighing in on the debate over gun control, which has been reinvigorated following the tragedy: “I am a father, the son of a kindergarten teacher, and an American. I was also born in Uvalde, Texas.”
In his op-ed, which acknowledges and supports the right to private gun ownership under the Second Amendment, McConaughey argues for measures he believes would prevent “dangerous people” from accessing firearms. He urged bipartisanship on the hot-button issue in American politics.
“There is no constitutional barrier to gun responsibility. Keeping firearms out of the hands of dangerous people is not only the responsible thing to do, it is the best way to protect the Second Amendment. We can do both.”
McConaughey won an Oscar for his role in the 2013 film Dallas Buyers Club, played a stripper in Magic Mike and starred in the first season of the crime drama True Detective.
He announced last November that he was removing himself for consideration for the governor’s race after months of considering a run.
But in a video posted to his Twitter account, he said he was honoured to have been considered for “political leadership.”
“It’s a humbling and inspiring path to ponder,” McConaughey said. “It is also a path that I’m choosing not to take at this moment.”
Governor Greg Abbott will take on Democratic nominee Beto O’Rourke for the position in November.
You can read McConaughey’s full op-ed here.