A frustrated John Smoltz called his agent in the winter of 2001 and gave him specific Bronx-themed instructions.

“(I) said, ‘Call the Yankees, tell him I’m going,'” Smotlz recalled to The Post’s Joel Sherman and Jon Heyman on the latest “The Show” podcast.

His agent, though, had made a promise to former Braves executive John Schuerholz that he would circle back to them before any decision would be finalized.

Those late talks ultimately swayed Smoltz, keeping him in Atlanta at the “buzzer” rather than joining the Yankees after their Game 7 World Series loss to the Diamondbacks.

Said Smoltz: “That’s how close it was.”

One of the most famous failed Yankees free-agent pursuits involves Smoltz’s ex-Braves teammate Greg Maddux, especially due to the ramifications it would have had for both franchises, and this Smoltz entry is a neat little “What if” to ponder from the early 2000s.

After starting all 356 games in his career through the 1999 season, the Braves transitioned Smoltz to a relief role in the 2001 season in his return from Tommy John surgery.

Over the final roughly six weeks, he served as their closer and tallied 10 saves.

Smoltz entered free agency that offseason wanting to return to the rotation, but the Braves instead wanted him to remain in the closer role.

Atlanta valued said role at three years and $21 million, which he viewed as below his value.

The Yankees, meanwhile, viewed Smoltz as a starter and he said Gene Michael — then the team’s vice president of professional scouting — offered a four-year, $52 million deal.

“The negotiations did not go well in Atlanta,” he said. “I was like, ‘Look, we’re not even close.”

Atlanta had one ace up its sleeve, though: Smoltz’s desire to remain in Atlanta.

He said he took less each time he stayed with the Braves during his career, but would be “boisterous” about it since he didn’t want to leave.

But the one year and extra $31 million marked quite the gap this time around.

“I didn’t mind taking a little bit less, but this was a little bit crazy,” he said.

The Braves ultimately upped their offer to $30 million over three years, which Smoltz accepted.

Smoltz noted that he wanted to be paid the same amount as Mariano Rivera, who made $9.15 that season and would make $9.45 million, $10.5 million and $10.89 million from 2002-04, respectively.

“Mariano Rivera is the best in our business. Nobody’s better,” Smoltz recalled. “But I’m not taking a penny less than him. It wasn’t arrogance, it was just like, ‘I don’t want to be the closer.’

“We ended up working it out at the buzzer.”

Smoltz ultimately served as Atlanta’s closer for the duration of that deal before returning to a starting role in 2005, and he remained with the Braves through the 2008 season.

He finished his career with the Cardinals and Red Sox in 2009.

The Yankees, meanwhile, still added veteran pitching that offseason in the form of Daivd Wells, in addition to signing slugging first baseman Jason Giambi.