Deontay Wilder was in line for a rematch with Brit Tyson Fury, who took the WBC world title from the American in February with a technical knockout win in Las Vegas.
However, Fury said last month he had "moved on" from a third fight with Wilder.
Asked on the Last Stand Podcast who he wanted to fight next if that was the case, Wilder listed former WBO world champion Parker as one of five opponents he was interested in.
Another Brit, Dillian Whyte, was at the top of Wilder's wish list, while Mexican-American Andy Ruiz, Ukranian star Oleksandr Usyk and Finnish fighter Robert Helenius were also mentioned.
The 27-2 Parker had already fought both Whyte and Ruiz, suffering an unanimous points loss to Whyte in 2018 and beating Ruiz by majority decision in late 2016 to win the WBO world title.
Ranked third with the WBO and sixth with the WBC, Parker was set to face fellow Kiwi Junior Fa in Auckland on December 12.