PHOENIX – Jesse “Bam” Rodriguez and Juan Francisco Estrada could be fighting for more than a junior bantamweight title.

A monster stepping stone could also be at stake.

Naoya Inoue, who enhanced his reputation as “The Monster” with his dramatic knockout of Luis Nery on Monday, was impossible to ignore Wednesday at a news conference for the compelling Rodriguez-Estrada fight on June 29 at the Footprint Center in downtown Phoenix.

On a stage just off the Phoenix Suns’ home floor, both fighters talked about big plans, all of which hinge on winning the World Boxing Council’s 115-pound version of the title.

The winner moves on, taking a step that could lead to Inoue, whose claim on pound-for-pound supremacy has never been stronger.

After the formal news conference, Rodriguez talked about Inoue, who is at the top of the pound-for-pound debate in a too-close-to-call race with Terence Crawford.

“I see myself fighting him one day,’’ Rodriguez said of Inoue.

Estrada, the WBC’s current 115-pound champion, is already talking about fighting Inoue.

He called out Inoue after his majority decision over Roman Gonzalez in a second rematch, in December 2022, also at Desert Diamond.

“He still wants to fight him,’’ Estrada’s manager/promoter, Juan Hernandez, said last December.

There were no formal talks for a fight with Inoue, Hernandez said. Instead, Estrada pursued a fight with Kazuto Ioka, the World Boxing Association’s 115-pound champion, who will face International Boxing Federation champ Fernando Martinez of Argentina on July 7 in Japan.

If Estrada beats Rodriguez, Hernandez foresees a possible fight with Ioka in Japan, in what could be the next step toward a date with Inoue. 

It’s still not clear what Inoue plans to do, however. He beat Nery at 122 pounds – junior featherweight. There’s speculation he’ll take the next step up the scale to the 126-pound featherweight division.

Rodriguez thinks he will.

“Yeah, I think he’ll get bored at 122 and move to 126,’’ Rodriguez said. 

There has been a lot of social media talk about lightweight champion Gervonta Davis facing Inoue. But the weight difference makes that one unlikely.

More likely: Inoue versus the Rodriguez-Estrada winner.

“Absolutely,’’ said Matchroom’s Eddie Hearn, the Rodriguez-Estrada promoter, who called Inoue-Davis a fantasy. “I like Bam fighting Inoue at 118 or 122 pounds.’’

At 24, Rodriguez, already a champion at 112 and 115 pounds, has room to grow.

“I want to unify the 115-pound title,’’ said the San Antonio fighter, who will be fighting for the third time in the Phoenix area, including a beatdown of Sunny Edwards for the flyweight title at Desert Diamond. “I figure on two, maybe three more fights at 115.’’

One possibility, Hearn said, could be the accomplished Roman Gonzalez, the lightest to ever be ranked No. 1 in the various pound-for-pound ratings. He has a fight scheduled against Colombian Rober Barrera on July 12 at home in Managua, Nicaragua. He hasn’t fought since his narrow rematch loss to Estrada.

Rodriguez trainer Robert Garcia foresees Rodriguez eventually moving up the scale. 

“One-hundred percent, we’re not looking past Estrada,’’ Garcia said Wednesday. “Me, personally, I’d like to see him go get the undisputed at 115. But if it’s 118, we could do that, too.’’

First, however, Bam has to beat the 34-year-old Estrada.

“Decision or knockout, my hand will be raised on June 29,’’ he said.

 But Estrada questioned Rodriguez’s unbeaten record (19-0, 12 KOs). He won the WBC’s junior bantam belt in a decision over Carlos Cuadras in February 2022 at Footprint. He defended it with an eight-round stoppage of Srisaket Sor Rungvisai about four months later in San Antonio.

“You have to say he’s a good fighter,’’ Estrada (44-3, 23 KOs), of Mexico, said through an interpreter. “But Rungvisai and Cuadras … I think those guys were on their way out.’’

But, Rodriguez counters, he has already heard that kind of talk.

“People didn’t think I could stop Rungvisai,’’ he said. “They probably didn’t think I could stop Sunny Edwards. They probably don’t think I can stop Estrada.

“But I’m a different breed. I’m a different animal. I’m here to shock the world.’’

For now, that world belongs to Inoue.