The pair, who both have Irish heritage and currently box out of America, are on the cusp of the world-title shake-up.
"Matthew and I have both fought recently, we're both from Ireland, we're both middleweights, we're similarly rated, we're both in a similar position in our careers," Sky Sports News quotes Lee as saying.
"So let's give the boxing public the fight they crave for and let the best man win. This is a massive fight in Ireland, Boston, Chicago or New York and will pack any venue. I am ready for the fight, we both have the same promoter, Lou DiBella therefore the fight can easily be put together.
"The fight would be a critical moment in both our careers, a win for either of us would propel us to a world title fight again, whoever wins the fight will go on and whoever loses the fight will have to either pack it in or start again."
Lee has a 31-2 record, while Macklin's figures stand at 30-5.