Some of their chats are strictly baseball.
"We talk a lot about what happens with this play or that one," Altuve said. "He'll let me know where he is, where he's going to be."
"We practice every single day, double plays, whatever," Correa said. "We've gotten to know each other a lot."
The payoff for this relationship was never clearer than during a moment in the top of the first inning on Monday night in a game the Astros would win 6-1. The Royals had runners on first and second with two outs when Kansas City catcher Salvador Perez hit a grounder up the middle that Altuve fielded nicely.
Altuve then flipped the ball back toward second base. Only thing is, no one was at second base when he released the throw. Correa, anticipating the throw, ran toward the base, caught the ball in stride and stepped on the bag for the third out of the inning.
"I gave 'em a hard time," Hinch said. "That might have been a little too casual, but it's fun to watch."
All of this has happened almost overnight. Correa, 20, made his big league debut on June 8 as the crown jewel of one of baseball's best farm systems. He played in just his 22nd game on Tuesday, and in that brief amount of time, has established himself as one of baseball's special players.
Correa is hitting .287 with nine doubles, five home runs, four stolen bases and an .852 OPS. And when Houston installed him across from the American League's defending batting champion, it might have constructed the best middle infield in the game.
OK, not everyone will agree with that. Here are four other teams that love their guys:
• Giants (Brandon Crawford and Joe Panik)
• Red Sox (Xander Bogaerts and Dustin Pedroia)
• Tigers (Jose Iglesias and Ian Kinsler)
• Cardinals (Jhonny Peralta and Kolten Wong)
Go ahead and make your pick. There are no wrong answers. These debates are a big reason we love this stuff.
Here's what's impressive about the Astros. It happened quickly. On the other hand, that's the story of the franchise in 2015. After averaging 104 losses the four previous seasons, Houston has been baseball's most surprising story.
At 46-34, the Astros lead the AL West by four games and have spent 76 consecutive days in first place. For more than a year, they debated the best time to begin Correa's big league career.
Correa began this season having never played a game above Class A ball, so Houston gave him a taste of Double-A (29 games) and Triple-A (24 games) before calling him up for the team's 59th game.
There was a financial component to the Astros' timetable -- arbitration eligibility, free agency, etc. -- but for a franchise suddenly shifted into a win-now mode, they also wanted Correa to be as prepared as possible. He has fulfilled every expectation and never looked overwhelmed.
"It's impressive," pitcher Collin McHugh said. "He's one of those guys you don't want to go to the bathroom when he's up to bat. You never know what he's going to do, but you know he's going to hit it hard somewhere."
One thing the Astros did was put their middle-infield duo near one another in the home clubhouse. They hoped that Altuve's professionalism and preparation would make an impression on the new guy.
Correa got the message.
"He's an unbelievable player, one of the greatest players in the game," he said of Altuve. "I've learned how to go about my business. He does it the right way. He works hard. He gets ready for the game during practice. He has a great routine, and that helps him be successful on the field."
How about that, Jose?
"I'm really enjoying it," Altuve said. "He's a really smart guy. Everyone knows what he can do. He's going to be a superstar."
Hinch believes Altuve and Correa have been good for one another, each helping make the other better.
"I'm not sure which one pushes the other more," Hinch said. "I think Altuve is introducing Carlos to the big leagues and pushing him to get acclimated quickly. I think Correa is pushing Altuve to be even better than he's been. They're good teammates -- to each other and to other guys on the team. It's as good a combo up the middle as I could ask for."