White denied that the UFC has stripped Jones of the title, as TMZ reported.
In a statement released Tuesday, the UFC said Jones' failed test stemmed from an in-competition sample that was collected at his weigh-in on July 28, the day before his fight against Cormier.
Jones tested positive for the anabolic steroid Turinabol, his agent Malki Kawa told "The MMA Hour." White did not comment on the banned substance for which Jones tested positive.
Kawa said that Jones thinks a tainted nutritional supplement could be behind the failed test, as Jones passed two other tests earlier in July.
TMZ was first to report news of the failed test.
"I always know what to say. I don't know what to say about this one," a somber White told reporters Tuesday, calling the news "unbelievable."
"These things never come at a good time. They're always bad, especially with somebody like Jon Jones. In my opinion, he's the best to ever do it. That makes it even more unfortunate."
Jones' camp released a statement Tuesday, saying, "We are all at a complete loss for words right now. Jon, his trainers, his nutritionists and his entire camp have worked tirelessly and meticulously the past 12 months to avoid this exact situation. We are having the samples tested again to determine the validity or source of contamination.
"Jon is crushed by this news, and we are doing whatever we can as a team to support him."
This is the second failed drug test of Jones' tumultuous career. The UFC was forced to pull Jones from a scheduled headliner against Cormier just days before UFC 200 in July 2016, after he tested positive for anti-estrogenic agents. Jones later told the U.S. Anti-Doping Agency that failed test was the result of an unmarked sexual enhancement pill.
Jones, 30, served a one-year suspension for the failed test. Before that, the UFC stripped him of his title in 2015 after he was arrested on hit-and-run charges. He is the only UFC champion to be stripped of a title because of disciplinary reasons.
Under the UFC's anti-doping program, multiple offenders face the possibility of a suspension doubled in length.
"If he ends up getting two or three [years], it might be the end of his career," White said Tuesday. "How old is Jon now? 30? And he'd be 33, 34 trying to make a comeback again? You look at what could have been and what he could've done -- it's sad."
If the results of the failed test hold, Jones' UFC 214 win over Cormier will be changed to a no-contest. Cormier, whose only two career losses have come against Jones, said Tuesday night that news of Jones' failed test was "very emotional."
"It's hard to find words to describe how I'm feeling right now," Cormier said in a statement. "I'm disappointed to hear the news. It's very emotional. We, as athletes, are entitled to due process, and I will refrain from saying much more until I know exactly what happened.
"In my mind, on July 29, I competed, and I lost. I thought Jon Jones was the better man that day. I don't know what to think anymore. I can't believe we are going through all of this again. We will see what happens next."
White also told reporters Tuesday that the UFC had been looking at a potential superfight between Jones and heavyweight champion Stipe Miocic in December before finding out about Jones' failed test.
Jones' win over Cormier at UFC 214 falls under the jurisdiction of the California State Athletic Commission.
CSAC executive director Andy Foster released a statement to ESPN saying that the commission is aware of Jones' failed test and will work with the USADA, which administers the UFC's anti-doping program, in its investigation.
"The California State Athletic Commission has been made aware of Jon Jones' test results and is looking into the matter," the statement read. "The Commission takes these matters very seriously and will take any appropriate actions necessary after a thorough review of the situation.
"As with all fighters, Mr. Jones is entitled to due process, and the Commission will work with [the USADA] to get all of the proper information."
Jones maintains the right to request that his "B" sample be tested to confirm the failed test. He also has the right to an appeal.
Before his win over Cormier, Jones adamantly denied accusations that he has used performance-enhancing drugs and said he resented Cormier for saying that he suspected Jones of longtime PED use.
"Daniel is trying to paint me as a steroid user. That's his biggest ammo," Jones told ESPN before the fight. "He can't say anything about my actual talent or skills.
"Out of all the things I've done bad, the thing I despise most [is PED use]. ... Steroids is something I've never done. And I don't want people chalking up a misunderstanding or a tainted supplement to me being a steroid user. It's one of the most insulting things you can do to a guy who's accomplished the things I've accomplished."