As previously reported, middleweight world champion Gennady Golovkin is closing in on a deal to fight Britain's Chris Eubank Jr.
Tom Loeffler told the Associated Press that both camps were "working on finalizing details".
The fight would take place in England in September, he added. WBC, WBA, IBO and IBF champion Golovkin, 34, has won all of his 35 fights and 32 of those wins have been by knockout while Brighton's Eubank Jr, 26, has lost just one of his 24 fights with 18 wins by knockout.
Eubank successfully defended his British middleweight title for the first time last week, with a fourth-round stoppage of the previously unbeaten Tom Doran. Earlier in the year he battered Nick Blackwell into retirement to capture the British crown.
Golovkin was in action back in April when he blew out IBF mandatory challenger Dominic Wade in two easy rounds at The Forum in Los Angeles, California.
"The majority of the terms are agreed, there's always stuff that needs to be done, but nothing appears to be a deal breaker," Hearn told Nick Parkinson.
"We're very close. I'm very hopeful the fight will take place and the Eubanks are deadly serious about it, this is not just to get their name out there.
"At the moment, both sides want to make sure everything is right, there are a lot of lawyers who need to agree to things, and it takes time to make a fight of this magnitude. If it happens, it will definitely take place in the UK.
"There's still a bit of a way to go but I'm confident everyone wants to make it happen. Let's see if they put pen to paper in the next few days. There's also Brook-Vargas and we are trying to marry the two together. I'm hoping the pair could be a month apart."
