Jones told MMA Fighting that a second fight between Holm and Tate was "never discussed" when Tate sat down with UFC execs recently.
It was announced Wednesday that Tate would defend her women's bantamweight title against Nunes at UFC 200 on July 9 in Las Vegas. Tate beat Holm for the belt at UFC 196 last month via fifth-round submission.
"A fight with Holly Holm was never discussed when we met with the UFC," Jones said. "We all agreed that Miesha should fight the best available and at this time it's Amanda Nunes, who is currently on a three-fight win streak."
On Thursday, Holm's manager Lenny Fresquez told the Albuquerque Journal that the UFC informed him before the fight was announced that it was Tate's choice to fight Nunes rather than Holm.
Fresquez told MMA Fighting that UFC CEO Lorenzo Fertitta called him before the announcement and told him Tate was the one who made the decision to face Nunes in her next fight. Holm wanted a rematch with Tate from the minute she lost at UFC 196.
"It was Miesha's decision," Fresquez said. "It was her decision to fight Nunes. That's what the UFC told me."
Tate told a different story to MMAjunkie on Thursday. The new champion said the UFC was the one who brought fighting Nunes to the table and she agreed to that.
"They thought that Amanda was the next best girl in line," Tate told Junkie. "They were like, ‘Look, you just beat Holly. You finished her.' They didn't feel that it was necessary to have an immediate rematch; it didn't warrant an immediate rematch. It wasn't one of those performances or such a crazy fight that we've got to have an immediate rematch."
UFC officials did not immediately respond to a request for comment on the situation.
Fresquez said Holm is "very disappointed" by the turn of events. She believed she earned an immediate rematch given that she was winning the fight heading into the fifth round. Tate is the only challenger in UFC history to go into the final round down on the cards and pull off the win with a finish.
"We'd like to see that fight," Fresquez said of the rematch. "We were expecting to get the fight. After all the trouble Miesha had getting a title fight, we gave her the opportunity. We feel like she took the easy way out, she took the easier fight."
The UFC and Holm's camp have butted heads over the last few months. UFC officials wanted Holm to wait before defending the title for the first time, until Ronda Rousey returned. Holm, who knocked Rousey out at UFC 193 in November, wanted to stay active and fight again sooner. Tate was the clear top contender.
After Holm lost, UFC president Dana White slammed Fresquez in the media for not waiting for the guaranteed big payday of a Rousey rematch. There is no love lost between White and Fresquez, but the manager said he does not believe Holm not getting a Tate rematch is retribution from the UFC. Fresquez said he appreciated Fertitta calling him before news of Tate-Nunes became public.
"I take Lorenzo at his word," Fresquez said. "This is what Tate wanted to do."
Fresquez questions Tate's claim that she was interested in fighting the best possible opponent in her first title defense.
"She said she wants the best fighters, but apparently she doesn't," he said. "She's definitely not cut from the same cloth as Holly."
Nunes also fought at UFC 196, beating Valentina Shevchenko by unanimous decision. She holds wins over Sara McMann and Shayna Baszler on this current three-fight winning streak and her lone UFC loss came against Cat Zingano in 2014.
Fresquez said he isn't sure what's next for Holm, because they were dead set on the Tate rematch. The UFC offered Holm a fight with Cris Cyborg at UFC 198, but Holm's team balked because she wanted the title shot. Fresquez said they would revisit the possibility of a matchup with Cyborg if she beats Leslie Smith at UFC 198 on May 14, but only under certain conditions.
"We would be interested in it," Fresquez said. "But not on an undercard or anything like that. It would need to be in the main event of a pay-per-view or something along those lines. We're only interested in big fights. If they offer us a fight that makes sense, we'll take it."