For Fa and his Kiwi manager Mark Keddell, the stars could be aligning. Joshua won't want a re-match against British rival Dillian Whyte to be his first fight in the United States as it would get far more hype at home, and he could see Fa, who is beginning to make his name in the US having fought there three times in the last 18 months, as a relatively low-risk opponent.
But having coped well in his sparring sessions against the dangerous Wilder late last year, and back in work with the American now, Fa will be confident of acquitting himself well against an opponent who could be rattled by a late change.
"Junior can knock out anyone in the world," Keddell told the Herald. "Junior is a very mobile heavyweight. He's done tons of rounds with Anthony Joshua as an amateur – as many as anyone outside the UK.
"Obviously Anthony is a better athlete now as he's older and more developed, but Junior certainly doesn't fear Anthony.
"We're in the right spot – Junior's in America right now sparring with the champion. Junior is ready to roll if we can make it happen."
Parker's only defeats as a professional came at the hands of Joshua, now the division's golden goose for the hype and money that follows him, and Whyte.
The step up in class for Fa would be enormous should he strike it lucky for the biggest pay-day of his career, but his training and health have also improved significantly and he looked good in knocking out Newfel Outah in the first round of their fight in Ohio last month. He will be waiting and hoping.