'The Gypsy King', who is poised to fight Anthony Joshua in a long-awaited bout later this year, made an appearance at UFC Freedom 250.
At a press conference, Zuffa Boxing president White was asked if Fury's presence was a sign he would sign a shock deal with the promotion company.
White, who is also the UFC CEO and president, replied: "We'll make an announcement soon."
Asked if that response meant the answer was yes, White said: "Listen, let me reiterate. Judge me January 1, 2027 on what we have done this year with boxing.
"All these other guys are talking a lot of smack. I haven't said anything about any of these guys. I haven't talked s*** about anybody or any other stuff.
"I'm in my lane. I'm doing my thing. Just sit back and watch. We'll make an announcement soon."
White was also asked about his potential involvement in the proposed Joshua fight, to which he replied: "For the last couple of weeks I have been hearing from the media and other people that I am not involved in the fight."
He later said: "It seems like everybody is always wrong."
Fury, who last fought in April when he beat Arslanbek Makhmudov at the Tottenham Hotspur Stadium, also teased the potential deal.
In an interview with UFC broadcaster Jon Anik, Fury said: "I think I'm going to let Dana do the speaking but it is a massive announcement."
Frank Warren, long-time promoter of Fury, did not comment on the speculation.
Asked if White may play a role in the Joshua fight, Fury said: "One hundred per cent potential, yes."
Fury added: "I'm very excited for this fight. It's been over a decade in the making.
"For whatever reason it hasn't happened before. Let's hope it happens right now, very soon."
Both Fury and White were pictured in Washington DC with Trump, who was hosting the event to celebrate his 80th birthday and the nation's 250th anniversary.
Justin Gaethje secured a big upset by beating Ilia Topuria, whose corner called for the fight to be stopped after the fourth round.
