Would El Pasoans Vote For Matthew McConaughey For Governor? Rumors have been swirling for months that actor Matthew McConnaughey may be running for Texas Governor and now there's more evidence he just might be. Matthew McConaughey is known as a Hollywood A-lister and Oscar winner, but could he also be trying to add "Texas Governor" to his list of accomplishments? If you believe a new report from Politico, he wants to. The news outlet is reporting that McConaughey has made at least two phone calls to two prominent Texas political influencers, a "deep-pocketed moderate Republican and energy CEO." The calls reportedly dealt with his serious thoughts on throwing his hat into the Texas Governor competition.