A studio spokesman on Monday said there was no further update.
The director's longtime publicist Simon Halls, meanwhile, told The Washington Post on Monday that he no longer represented the director and declined to explain why.
The representative for Graham King, the producer-financer for whom Bohemian Rhapsody has long been a passion project, did not respond to a request for comment.
Rhapsody centers on the band's early years, culminating in its seminal Live Aid performance in 1985.
Some outlets have cited a statement from Singer's lawyer that noted medical concerns.
"This is a personal health matter concerning Bryan and his family. Bryan hopes to get back to work on the film soon after the holidays," the statement said.
A call by The Post to Singer's lead attorney, the Los Angeles-based David Feldman, was not immediately returned.
For now, the movie remains in limbo as Twentieth Century Fox's chairman and chief executive, Stacey Snider, must decide whether to wait for Singer or bring on a replacement director for the film, due out next Christmas.
The situation is somewhat akin to when filmmaker Zack Snyder left Justice League due to a family tragedy and had to be replaced in postproduction by Joss Whedon; in that case, at least, the movie had completed shooting.
Singer, 52, has been one of Hollywood's more reliable moneymakers, with his past two X-Men movies each grossing at least US$500 million worldwide.
But a raft of allegations of sexual misconduct have long followed him, including several lawsuits by teenage boys accusing him of misconduct in work environments.
None of the entertainment trade publications were able to parse the disappearance, though some pundits couldn't help speculate about it in context of the allegations of sexual abuse.
Those allegations have resurfaced in the wake of Hollywood's harassment scandals, and were fueled when the actress Jessica Chastain tweeted last month "let us never forget" in reference to an article about Singer. She has not shied away from those sentiments since.
The disappearance from the set of the New Jersey native, who directed artier fare such as The Usual Suspects and Apt Pupil before shifting into superhero mode, echoes other cases of directors who kept a distance from their set, to the chagrin of their collaborators.
The Grace of Monaco (2014) director Olivier Dahan was said by the film's writer to spend long stretches in his trailer. While directing 2009's The Fantastic Mr Fox, Wes Anderson kept his distance in Paris while the film shot in London, to the annoyance of the crew.
Rhapsody has had a tortuous backstory. It was in development as far back as 2010; a conversation with producer King six years ago this month had him talking about its imminent production.
Numerous actors, including Sacha Baron Cohen and Ben Whishaw, were attached to play Mercury, and the number of writers and directors involved with it is nearly as long as Queen's list of top 40 hits.
King's deep investment the project ensures the show will go on, though how it will break free remains in question.
