The news comes a day after Radio City announced plans to move its New York Spectacular from spring to summer, with performances scheduled to begin June 15, 2016, just a week after the Tonys, which are planned for early June.
The elaborate, multi-media production will be in its final week of rehearsals.
The Times reported that "barring a last-minute change of heart" by Madison Square Garden Company (MSGC), which manages Radio City, the ceremony will return to the much smaller concert venue, the Beacon Theater, which has less than half the seats, 2,900.
A spokesperson for the Tony Awards offered a glimmer of hope for the future of the Tonys at Radio City, telling Playbill.com, "The location is still in negotiations for any venue options.... We are still in negotiations and will announce that location when the deal is completed."
The change would be a disappointment for the Broadway community, which counts on the extra seats, not just for industry people who want to attend Broadway's biggest night, but for fans who were able to buy tickets in the upper balconies at the larger venue.
No word on whether any tickets would be sold to the general public for the Beacon.
The Tonys were held in Broadway theatres until the late 1990s when they switched to Radio City for the first time. A scheduling conflict with Cirque de Soleil led to the ceremony being switched to the Beacon (also owned by MSGC) in 2011 and 2012, after which Radio City became available once again.