Parker is keen to get a fight before the end of the year with likely opponents being Joyce or fellow Briton Derek Chisora.
Joyce is next in line to challenge for the WBO belt after Anthony Joshua defends his world titles against Oleksandr Usyk at Tottenham Hotspur Stadium on September 25.
Joyce’s manager Sam Jones told Sky Sport UK they’d face the New Zealander “in a heartbeat”.
The British contender could risk his status as WBO mandatory challenger against Parker, who is also ranked highly by the WBO.
