Alastair Cook has long been Andrew Strauss's heir apparent as captain but the latter's retirement on Wednesday also leaves a spot at the top of the order ahead of the tour to India in November.
And Vaughan believes Root, who has scored over 600 first-class runs this season for Yorkshire at an average exceeding 55, could thrive, saying: "Joe has come from my club in Sheffield, the same system, and I'm good friends with him and his family.
"I'd love to see him get the call and India's not a bad place to get going as an opening batsman.
"He's a solid player, a solid character and a very good individual to have around. He has all the traits to withstand the pressure of international cricket."
England were expected to name their Test squad for India in the next fortnight but may now choose to delay that as they ponder how best to replace Strauss.
Whether or not Root gets the call, Vaughan has advised the selectors to opt for a specialist rather than shunting Jonathan Trott up a place.
"I would rather see England promote an opener from county cricket than move Jonathan Trott from three to two," he said.
"He is such a calm, consistent influence at three so I would want to keep him there and identify the best opener.
"(Michael) Carberry will get a mention, I've heard (Nick) Compton mentioned and there's Joe but there aren't many other options. A lot of the good young players around are middle-order players.
"But opening is something you need to do for most of your career and it's not easy to convert. I hope they go for someone who has been playing as an opener."
- Andrew Strauss