Irish Prime Minister Says Conor McGregor Could Have a Future in Politics

Don't laugh off Conor McGregor hitting the campaign trail -- 'cause one of the most powerful members of Ireland's government says the Notorious could totally run for office!

We got Irish Prime Minister Leo Varadkar out at SXSW in Austin ... and he told TMZ Sports it'd be crazy to rule out the UFC megastar parlaying his popularity into a political career -- something McGregor hinted at recently.

Varadkar knows about defying the odds -- dude was Ireland's first openly gay and ethnic minority PM when he was elected in 2017, not to mention the youngest one in the country's history.

Leo also just met Arnold Schwarzenegger (which we got on video) -- and said if The Governator could do it, why not Conor??