Parker, who Anthony Joshua defeated in 2018, will return on January 21 against Jack Massey, on the undercard of Chris Eubank Jr’s fight with Liam Smith.
But the former WBO champion is eyeing revenge against his British rivals after returning against Massey in Manchester.
“There wasn’t a lot in it. If I can get a good win over Jack, that could be next.
“David Higgins, my manager, sent a message to Matchroom [to ask] if Joshua needed a fight but we got no reply back.
“He’s got to fight someone. I know he’s looking for a trainer or working with a few trainers in America but if AJ wants a fight, let me finish Jack off, if you’re looking for a fight, come to me.
“Dillian Whyte, if you’re looking for a fight, I’m available, after I take care of Jack.
“Even Joe Joyce, if you want another fight and no one wants to fight you, let’s go again. I don’t really care. I have no worries about fighting anyone.”
Whyte, 34, most recently returned in a disputed majority decision win over American Jermaine Franklin, 29.
AJ is yet to return to the ring since losing his Saudi Arabia rematch with Oleksandr Usyk, 35, in August, his second defeat to the Ukrainian in 11 months.
He is expected to return by April against a top 15-rated contender before moving onto a rematch with Whyte.