White told TMZ Sports Thursday it's "highly unlikely" Jones' B sample will show anything different upon examination.
The UFC announced Tuesday Jones tested positive for a banned substance after being tested July 28 following his weigh-in ahead of UFC 214.
Jones beat Daniel Cormier at UFC 214 to claim the UFC light heavyweight championship. TMZ Sports initially reported UFC had stripped Jones of the belt following his positive test, but ESPN.com's Brett Okamoto spoke to White, who confirmed Jones will keep the title for the time being.
The United States Anti-Doping Agency banned Jones for a year after he tested positive for clomiphene and letrozole. Because of that previous infraction, the Los Angeles Times' Lance Pugmire reported Jones may miss up to four years as a result of his second positive test.
White openly questioned whether UFC fans have seen the last of Jones entirely.
"If it ends up getting two or three (drug violations), it might be the end of his career," he said, per MMAjunkie's Steven Marrocco and John Morgan. "So to talk about his legacy, it's probably the end of his career."
Jones turned 30 in July, so a multiyear absence from mixed martial arts would potentially be devastating to his career. By the time he returns, he'd have to rebuild his trust with White, who said last November Jones was never going to headline another UFC pay-per-view. White relented, with Jones leading the UFC 214 card alongside Cormier, but White may not be so forgiving again.