KANSAS CITY, Mo. — After trying to trade for Manny Machado last July and then pursuing him less fervently as a free agent during the offseason, the Yankees will host him again Monday when the Padres visit Yankee Stadium.

And even though Machado’s former teammate in Baltimore, Zack Britton, never got the feeling Machado would join him with the Yankees when they were both on the open market last winter, the reliever still believes the third baseman would have been a “perfect fit” in The Bronx.

“I talked to him a lot during the [free-agent] process,’’ Britton said Sunday before the Yankees finished their road trip with an 8-7, 10-inning loss to the Royals at Kauffman Stadium. “It was a long process and just in conversations with him, I don’t think either of us thought it was gonna work out here based on what he told me with the talks.”

That doesn’t mean Britton didn’t think Machado wouldn’t have thrived with the Yankees.

“I thought he was a perfect fit,’’ Britton said. “He brings elite defense at third, his power in the Stadium would have played and he would have been good in the clubhouse where there are other big names, as well.”

And while Machado visited the Yankees, along with the White Sox and Phillies, he ultimately got his mega-deal with San Diego worth $300 million over 10 years.

“It would have been nice to have him, but with the money and our high payroll, I get it,’’ Britton said.

Even with Miguel Andujar out for the season with a torn labrum in his right shoulder, the Yankees have seen Gio Urshela thrive at third.

Urshela was unable to handle a bad hop on Whit Merrifield’s game-winning single Sunday, but has been superb defensively since taking over for Andujar. And he has emerged as a solid offensive player.

“You couldn’t ask for more than what Urshela is doing,’’ Britton said. “I don’t know if anyone could have given us more production to this point. Manny is elite at everything, but I can’t think of one thing Urshela has done that you could have gotten more of from someone else.”

Still, there’s part of Britton that wishes Machado had ended up in a more high-profile spot than with the Padres, who are in the hunt in the NL wild-card race.

“He’s that guy, if you put him on a big stage, especially when he wants to prove something, he’s great,’’ Britton said. “He’s not there now. Those types of players should be on the big stage.”

He will be, though, this week.

“It will be good to see him,” Britton said. “I hope he doesn’t do any damage against us. I know he’s gonna turn his game up.”