Sir Bob Jones, however, has preached caution over the hype surrounding his former charge.
Sir Bob, who managed the fighter until last year, insisted little significance could be read into Parker's knockout victory.
He said neither Parker's record nor the ratings were of particular importance.
"Joseph is working his way along nicely, he's very young and there's plenty of time," Sir Bob said. "But this claptrap about world ratings is just childish.
"I get pretty angry with this 'No10 in the WBA' nonsense. Joseph at this stage is unrateable because he's too new and so far he's fought a series of nonentities."
Sir Bob hopes Barry will help to ensure the right opponents are now chosen for Parker.