Billy Joe Saunders would fight Gennady Golovkin "in his garden", says the Briton's promoter Frank Warren.
He told BBC Sport talks have taken place with the Kazakh fighter's camp over a unification fight between the two undefeated middleweight champions.
Saunders, 28, could face Golovkin in June, instead of his scheduled fight with fellow Briton Martin Murray.
Golovkin was due to fight Saul Alvarez on 5 May in Las Vegas, but the Mexican withdrew from the rematch on Tuesday.
Alvarez is awaiting the outcome of a hearing into an adverse drug test.
WBA, WBC and IBF champion Golovkin, 35, said on Wednesday that Alvarez's replacement would be named soon, adding he would still be defending his titles on 5 May in Las Vegas.
That date would be too early for Saunders, who is unable to spar until 14 April after picking up a hand injury, which caused the postponement of his WBO defence against fellow Englishman Murray until 23 June.
"We have had conversations [with Golovkin's camp] and will speak later today and see where it goes," said Warren.
"Provided Golovkin would be willing to fight in June, Bill would be available.
"I understand they are looking at 5 May in Vegas, but I am not sure if they will find an opponent or sell a show out in such a short space of time.
"I am hoping they will take the fight, then we can do it here or go to the States, but that will be their call," added Warren, who said a fight in England would "have to be a stadium fight".
Warren says the fight would have to be agreed "sometime this week".
He said: "We need to know soon and not let it drag on. There is a short window to do it and we need to get a decision.
"In the meantime we have not postponed the Murray fight, but if this one comes up in between obviously we would consider it, provided the terms are OK. Bill would like to fight Golovkin, there is no doubt about that.
"Bill said he would fight him in his garden."
Warren said a contract was agreed for the two to fight last year, but Golovkin was instead rested before his first fight with Alvarez in September, which ended in a controversial draw.
"Golovkin has stated many time he wants to fight Bill. Bill wants it, Golovkin says he wants it. I do not know if Golovkin's management wants it. There should be no problem making it - on paper it is a great fight."
Despite Golovkin's record of 33 knockouts from 37 fights, Warren believes Saunders could beat him.
"This is a fight that will define his legacy and I genuinely believe he can win. But he has to be 100%, I am not having him get in there with a hand injury."