One reason why the Manny Machado-to-the-Yankees freight train is a resonance throughout the game is that their public praise of Miguel Andujar is not matched by their private evaluation.

Multiple executives told The Post that Andujar’s free-swinging penchant and poor defensive metrics are areas of concern, with one saying, “Andujar is a horrendous third baseman. This all feels like the Yankees building up a player’s value to trade him for a young, controllable starter and then they will revisit the issue of third base in the offseason with [Brandon] Drury, an outside third baseman or signing Machado.”

When presented this, GM Brian Cashman said: “That is completely false. I think [Andujar] is a hell of a player. We have said ‘no’ to him [in trade talks] not just this year but from Double-A on up. I have not included him any deals and that should say how I feel about him.”

During the offseason, the Pirates requested not just Clint Frazier (with whom the Yankees were willing to part) but Andujar for Gerrit Cole and the Yankees rejected the overture. The Rangers are among several teams that have inquired multiple times about obtaining Andujar.

So is Andujar untouchable between now and 4 p.m. July 31?

“I said that with Gleyber Torres [a few weeks back] and that was a mistake because it leads to follow-up questions that are not worth me dealing with,” Cashman said. “I am not going make the same mistake [pronouncing someone untouchable] moving forward. We value [Andujar] a great deal.

“We have been challenged many times to move him or coerced to move him. He is here because of what we think of him. And I mean ‘we.’ His makeup is off the charts. His work ethic is off the charts. His energy is off the charts. And his physical ability is off the charts. He is a major contributor, which is what we thought he’d be.”

Andujar went into Friday with 41 extra-base hits in 81 games, which not only was nine more than any other rookie, but were the same total as Giancarlo Stanton (91 games) and one more than All-Stars Jose Abreu (90 games) and Nick Markakis (91). His OPS, 17 percent above the MLB average factoring in league and park, was better than that of Justin Upton, Cody Bellinger and George Springer.

However, Andujar also had drawn just 15 walks in 327 plate appearances and the metrics on FanGraphs have Andujar as by far the worst defensive third baseman of the 21 qualified.

“I don’t think there is a defensive issue now,” Cashman said. “I am not analytics-driven on this. I think he is an above-average player at that position at a young age. Whatever his deficiencies, he can improve on them, like Robinson Cano was able to develop into a bigger, better player for us. If he is a free swinger, his chase rate will improve. If he has defensive deficiencies, they will improve. Because he already has. Where he was and where he is now, I feel vindicated not moving him.”

Several teams are pursuing Machado, but the Yankees are the only ones who would ask him to shift from shortstop (where he has stated he wants to play) back to third, where as opposed to short, Machado had been an elite defender. In theory, Machado would not only help the Yankees with his brilliant bat, but with golden defense, too, at the hot corner, where Andujar struggled more overtly last year than this season.

“I was not as worried as others,” Cashman said about defensive issues that arose last year, especially with throwing — Andujar does throw with an unorthodox slinging motion. Cashman said he acquired Drury as a hedge in case Andujar needed more seasoning.

But while Drury was sidelined because of migraine issues, Andujar came up and seized the job.

“The same as Cano and [Alfonso] Soriano,” Cashman said. “Those guys showed up and said, ‘No, my time is now.’ Miggy is doing that now. The proof (of how the Yanks feel about Andujar) is in the pudding. We are huge Andujar fans and we have demonstrated that by not trading him despite how many offers we have had to do so. The dude is only 23 years old. Whatever that narrative is (that the Yanks are building him up to trade him) is a false one. I am a big fan of this guy. Not just me. It is we are big fans.”