Rumours that Matthew McConaughey is considering a run at becoming governor of Texas are heating up amidst a report from Politico that the “Dallas Buyers Club” Oscar winner has been “quietly making calls to influential people in Texas political circles, including a deep-pocketed moderate Republican and energy CEO, to take their temperature on the race and to talk about seriously throwing his hat in the ring.”

If McConaughey does decide to run, political consultant Karl Rove (who guided former Texas governor George W. Bush to two terms in the White House) predicts a tough path forward.

“I find it improbable, but it’s not out of the question,” he said of a McConaughey victory.

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However, Republican strategist Brendan Steinhauser thinks that the old guard in Texas political circles might be underestimating McConaughey’s popularity in his home state.

“I’m a little more surprised that people aren’t taking him more seriously, honestly,” said Steinhauser. “Celebrity in this country counts for a lot… it’s not like some C-list actor no one likes. He has an appeal.”

Meanwhile, McConaughey has yet to give any indication as to what party he would affiliate with.

“The question is: Would he run as a Republican? A Democrat? Independent? And where is he on the political scale? He says he has a funny phrase about being a hardcore centrist, but what party would he run under?” said Rove.

Gilberto Hinojosa, chair of the Texas Democratic Party, said that his party would “welcome” McConaughey if he decided to run as a Dem.

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“He’s young, good-looking, smart and has a little wildness — but this is Texas. We like that stuff,” Hinojosa said. “He has not reached out to the party that I know of. It’s absolutely up in the air.”

However, he also warned of what would likely happen if McConaughey were to run as an independent. “If he wants to run as an independent, he’d be a spoiler and guarantee [incumbent Republican governor Greg] Abbott gets elected,” Hinojosa added.

A spokesperson for McConaughey did not comment on the record for Politico‘s story.