Dominic Chappell crticised Green, saying he effectively blocked a rescue bid by Mike Ashley for BHS - a claim later denied by Green's Arcadia group.
Green was scheduled to appear before MPs on June 15 but on Friday said he was "not prepared to participate" unless Frank Field MP, the chairman of the Commons inquiry into the affair, resigned.
The same Commons Committee also quizzed Ashley last week over working conditions at Sports Direct.