David Price says he hates no one and no team. He will not go into his first Red Sox-Yankees rivalry start Sunday with any malice toward the Yankees. That’s just not him.

“I can’t go out there with negative thoughts or hatred for someone,’’ Price says. “I don’t need added adrenaline. I don’t treat any team differently. I go out there and think they’re all All-Stars.’’

Curt Schilling might have said, “I guess I have to hate the Yankees now’’ at his introductory press conference with the Red Sox, but Price just sees it as the next opponent. Maybe when he’s on the mound and feels the crowd and hears the boos every time Alex Rodriguez or turncoat Jacoby Ellsbury comes to the plate, he may have a different feeling.

After all, we have seen the amped-up Price, especially when he faced the Red Sox and especially against David Ortiz in those hostile days between the Rays and Sox. Price acknowledges the Red Sox-Rays rivalry was huge for the Rays. It pitted small-market team vs. big-market team.

I asked Price what nasty things the Rays used to say about the Red Sox back then and he quipped, “They’ll just go buy somebody.’’

Ha.

It turned out they bought Price, for $217 million.

“It’s going to be fun,’’ Price said. “It’s a place [Fenway] I’m familiar with. I spent a lot of time in the AL East in my career. It’s been good. It’s a rivalry I’ve seen all my life as a fan of the game of baseball and now I get to witness it firsthand on the mound.’’

Other than Rays-Red Sox, the only other rivalry Price was involved with was his alma mater Vanderbilt vs. Tennessee. But even then Price didn’t hate Tennessee. He got up for those games for sure, and normally the games meant something so they were intense. But being the best pitcher then and being the best pitcher now, there wasn’t much difference in his demeanor. He was expected to pitch a great game.

And that’s what he wasn’t doing enough as he started his Red Sox career. He straightened that out with an eight-inning, two-run, 14-strikeout performance against the hapless Braves.

But now he’s facing the Yankees, a team he’s pitched well against in the past.

Someone asked Price how he’d pitch Rodriguez and he said, “I’m not going to tell you. He knows how I’ll pitch him.’’

Price’s other big duty when not being ace of the Sox’ rotation is mentoring other pitchers on the staff. If only he could turn Clay Buchholz around.

When Price was young, James Shields was a huge influence on him. He mentioned how Shields, along with Scott Kazmir, Edwin Jackson, Andy Sonnanstine, and others, took him under their wing, even though “I was trying to win a job from them,’’ and showed him how things were done in the big leagues.

He in turn did that with Chris Archer and Alex Cobb and Matt Moore.

When Price got to Toronto he took Marcus Stroman under his wing.

Archer said recently Price still texts before every start to wish him luck and get his spirits up.

In Boston, Price has already connected with Eduardo Rodriguez. The two spent a lot of time together. It seemed like the perfect union of the lefty who may at the top of his game vs. the lefty who could become one of the best in time.

“He was way ahead of me,’’ Price said. “At his age I threw a fastball, slider. He’s got a fastball, changeup, curveball, slider. He’s got four pitches he can throw any time in the count. I just watched his bullpen [session] and he’s special.’’

Archer said that’s what Price does — he builds you up and makes you trust your stuff to the point you come out of a conversation with him thinking you’re the greatest pitcher of all time. The Price/Eduardo Rodriguez relationship should be fun to watch over time.

While pitchers rely on the pitching coaches and catchers for support and instruction, there’s nothing like the influence of a big star to help shape what could become greatness. Eduardo Rodriguez also spent time with Pedro Martinez in spring training, so the influences of Martinez and Price could be huge to what Rodriguez eventually becomes.

“Any time I can offer my help, or knowledge or wisdom, call it what ever you want, I’ll do it,’’ Price said. “Everyone is different. Everyone throws a pitch a different way. If someone needs help on a certain pitch and asks me how I throw it, I’m glad to share that, though that might not fit exactly for that guy. But like I said, I’m here and I’ll always offer my support. You can bank on that.

“If more is asked for, I’ll give it. The better your pitching, the better your team. We’re in this together as teammates. That’s the way I’ve always felt. I spend a lot of time talking to hitters and getting their sides of things. I think it’s important for pitchers to talk about hitters and their mind-sets. That can only help you as a pitcher and getting an idea of how they think on a certain count.’’

Price, who is 13-7 with a 4.04 ERA in his career vs. the Yankees, certainly won’t be awed by the attention of his first Red Sox-Yankees start on ESPN’s “Sunday Night Baseball.’’ He was brought in to pitch in these moments. And for Price, it’s just another day at the office.

Nick Cafardo can be reached at cafardo@globe.com. Follow him on Twitter @nickcafardo.