The UFC doesn't deserve the greatness that is a_ok_i.
Besides, between the DREAM, Shooto, WAMMA, and ONE belts, the amount of great victories he has, and the amount he's getting paid to teach at EVOLVE and to take part in the Japanese end-of-year celebrations, he doesn't need the UFC.
He'd only need the UFC to prove his worth to the moronic fans who called him a cancrusher when he was beating Hansen, Alvarez, JZ, Kawajiri, Kikuchi, and a bunch of others, while they were simultaneously hailing BJ Penn's wins over Diego Sanchez and Kenny Florian. Most of those people would still insult Aoki's accomplishments even if he came in, grapplefucked everyone and won the UFC title, so their view of him doesn't really matter.
He also said he was offered a UFC contract years ago, but the other offers he was getting were more enticing, so he didn't take it. And it's been hinted that connections with the Yakuza have prevented further negotiations with the UFC in recent years.
Even if they weren't, though, he's had such a good career and he's got such a good thing going for him right now-- he gets paid a lot of money (especially since there's no sponsor limitations), gets to travel, gets paid to train with the best people in the world and improve as a martial artist, fight solid opponents in ONE and fulfill his competitor's desire-- that he doesn't need to go to the UFC.
I also don't think he has anything to gain by going to the UFC. Unless they give him an immediate title-eliminator, it'll take so much effort to get even a title shot and get to the same place in the UFC that he is outside of it that it's hard to see the upside as anything other than the "You won't get this now, but you may get this in a few years if you do all of these things first" back-end deal kind of way.
He's also not fighting overmatched opponents as purely as people think. He's fought a few overmatched opponents, but, of his last 9 opponents, only Toshikatsu Harada and Yuki Yamamoto were the ones that were really overmatched, and maybe Sakuraba and Cody Stevens. But it's hard to call them cans since Stevens had a good record and some nice wins, and since a lot of people thought Aoki's wrestling was so terrible and his chin was so glass that Sakuraba would easily stuff his takedowns and KO him, it's hard to call Sakuraba a totally-overmatched opponent, too.
All of Aoki's other victories-- Ando, Boku, Mckee, Lepont, Shalorus-- are all very solid, good, accomplished fighters with solid records, albeit with limited name-recognition to a lot of people, and were all very good victories.
A lot of people who knew about Shalorus and Ando were also so convinced of Aoki's terrible wrestling and even-worse chin that they thought he'd be incapable of taking down either of them-- since Shalorus has a solid wrasslin' background and Ando's a very strong Jūdōka-- and they'd easily KO him or outstrike him to a decision.
If Tynanes re-signs with ONE, he'll have another strong opponent to fight in the near-future, and there's a handful of other strong guys in ONE that he could end up fighting aside from him.