"They're his three main choices and I expect him to make his mind up in the next seven to 10 days. He's a smart young man and the final decision is always made by him," BBC Sport quotes the promoter as saying.
Wilder has personally expressed interest in setting up a bout against Joshua, but his management team are yet to table a formal offer.
Unbeaten Joshua recently called out Wilder's camp to prove that they have the money to make the fight happen.
Joshua, who has won all 21 of his professional fights so far, is expected to name his next opponent within the next 10 days.