The duo currently hold all the belts in the heavyweight division with Usyk holding the WBA super, WBO, IBF and IBO titles and Fury holding the WBC belt.
There has never been an undisputed champion in the division since the WBO belt was added as a major title in 2004. Lennox Lewis was the last to be undisputed in the four-belt era with his unanimous win over Evander Holyfield in 1999.
Usyk’s manager Alex Krassyuk issued an update on Instagram insisting the fight "should happen no later than March 4. Location: Any place in the Universe."
"Both parties agreed to fight," he added, before commenting it should take place "sooner the better."
After beating Derek Chiosra in early December, Fury said he was considering undergoing surgery on his elbow which would delay his clash against the Ukrainian beyond the March deadline.
"According to our knowledge, Tyson Fury is safe and sound,” Krassyuk said.
The fight will reportedly take place in Saudi Arabia with officials in the Middle East keen to bring a high-profile heavyweight bout to the region.