WBA and IBF heavyweight champion Joshua is 20-0, all by knockout, following his win over Carlos Takam in Cardiff in October.
Last month, Wilder retained his WBC crown by flooring Bermane Stiverne in the first round to move to 39-0, and Joshua's promoter Eddie Hearn reportedly held talks with the American's representatives about a potential meeting next year.
Joseph Parker, the WBO champ, is also in the mix for a unification bout with Joshua in 2018, and the New Zealander is happy to settle for a 35 per cent share of profits - a notion Wilder will not entertain.