Preparations for the July 24 heavyweight bout in Las Vegas have been thrown into doubt due to a coronavirus case in Fury’s camp.
Promoters Top Rank said they were monitoring the situation closely, with an announcement expected later on Friday.
“As soon as we have word, we will be putting out a statement,” Top Rank media relations director Evan Korn told the PA News Agency.
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Fury beat American Wilder to become WBC heavyweight champion in February last year, 14 months after the two men fought a thrilling draw.
The Briton has been training in Las Vegas in preparation for their third contest.
Fury, 32, had looked set to be heading into an all-British heavyweight showdown against Anthony Joshua in Saudi Arabia during August.