Hudson has already signed All Whites Kip Colvey, Deklan Wynne and Tommy Smith, as well as assistant coach Darren Bazeley, so Krishna would be another New Zealand-based addition to that roster.
A move would have been massive for Krishna. He would have become the first player from an Oceania Island nation to play in the MLS, and could probably have doubled his salary. The MLS salary cap is US$4 million (A$5 million), while the A-League's is A$2.9 million.
It would also have been a chance to display his talents on a much bigger stage, and would have capped a fairy tale rise for Krishna, who grew up in the town of Labasa, on a different island from Fiji's main centres, before coming to this country as a teenager.
Krishna would have also arrived to some familiar faces at the Rapids, with his long history in the national league under coaches Neil Emblen and Bazeley at Waitakere United.
The potential move may have been complicated by the Phoenix's current predicament. They are bottom of the table, and Krishna has been one of their best offensive weapons for the past few years.
The 30-year-old has an impressive record, scoring 32 goals in 86 games for the Phoenix, second only to Paul Ifill (33 goals) in the club's history.
Making it even more noteworthy is that Krishna has spent most of his time in the A-League on the wing, from where he has also contributed 21 assists (behind only Leo Bertos and Ifill in Phoenix history).
The Wellington club were probably also burnt by their recent experiences with Kosta Barbarouses and Dario Vidosic. They received no compensation for either player and the duo have gone on to perform well with rival A-League clubs.
Phoenix chief executive David Dome confirmed it was their intention to re-sign Krishna, whose contract finishes at the end of this season.
"We want Roy to stay," Dome told the Herald on Sunday. "We will try our hardest to keep him at the Phoenix. We rate him as a player and leader."
Dome wouldn't comment on Krishna's transfer fee, saying it was a private matter.
Krishna, who has also scored 20 goals in 32 games for Fiji, was a late withdrawal from last Saturday's match against Adelaide United due to a hamstring strain.
He also didn't travel for Friday night's 4-0 loss at Sydney FC, though coach Darije Kalezic is unclear about the extent of his injury. Scans in Wellington weren't conclusive, so Krishna has travelled to Auckland for a second opinion.