Joe Joyce v Joseph Parker could be made this year if the Kiwi accepts the offer.
Joyce, the number one WBO heavyweight contender, is recovering from a wrist injury but hopes to return before the summer.
Reports suggest that Parker is no longer working with Matchroom and is now free to explore other options after his two wins against Dereck Chisora.
The 30-year-old recently called out Andy Ruiz in what would be a rematch from their 2016 fight for the WBO heavyweight title which Parker won in New Zealand. However, his manager David Higgins revealed that Joyce’s team had been in touch about a potential bout in May.
“The Joyce team have reached out to us and said they’re going to make a written offer,” Higgins told Sky Sports.
“Both sides have talked about May timing, so we’ll see what that offer looks like.”
Parker sits one spot behind Joyce in the WBO rankings while the two men sit in the same order but at two and three with the WBC.
Joyce (13-0, 12 KOs) has wins against Daniel Dubois and Carlos Takam in his last two fights and sits in a great position to get a shot at the WBO title currently held by former amateur opponent Oleksandr Usyk.
A fight between Joyce and Parker (30-2, 21 KOs) makes sense but Higgins says his fighter is also keen to make a name for himself in America just like his friend and training partner Tyson Fury.
“Joseph has said he’ll fight any of the big name and high-ranked Americans from Deontay Wilder to Andy Ruiz to Luis Ortiz to Michael Hunter, any of them we would look at,” said Higgins.
“My job now is to model up what the American opportunities would look like, but right now to model up what the Joe Joyce opportunity would look like, so it looks like we’ve got a few options.”