The Dublin stadium's chief executive Peter McKenna claimed last week that the all-British bout could share the bill with Irish legend Katie Taylor's farewell fight but Hearn insists that Taylor will be the main attraction for her swansong.
Speaking on Matchroom Boxing's social media channel, Hearn said: "There is nothing else on the agenda apart from Katie Taylor.
"Anthony Joshua against Tyson Fury, for me, is not going to happen at Croke Park.
"Katie Taylor is not fighting on any undercard. If there is a fight at Croke Park, it should be Katie Taylor and Katie Taylor only.
"That is the whole story; that is the history, the legacy and nothing short of what she deserves, so on Friday (17.04.26), we will be at Croke Park to try and advance those talks."
Taylor has frequently expressed a desire to fight at Croke Park before her retirement and Hearn insists that he and his team will "do everything we can to make it happen" for the 2012 Olympic gold medallist.
The promoter said: "There's massive public demand and momentum for this to happen.
"Katie Taylor has made it clear she wants to fight one final time. She has done everything in the sport you can do: she's European amateur champion, world amateur, Olympic gold medallist, world champion, unified champion and undisputed champion.
"She's sold out Madison Square Garden, boxed at Wembley Stadium, the Millennium Stadium, so this is the moment Irish sport stops and pays homage to not just one of the greatest people of all time, but one of the greatest athletes ever to come out of Ireland.
"She deserves this so much and we'll do everything we can to make it happen."