Hayne quit the NFL on Monday in a bid to play rugby union sevens at the Rio Olympics later this year.
Speculation is rife he will return to rugby league next year, after leaving in 2014 to pursue his American dream.
Sydney Roosters, who are around $600,000 under this year's salary cap - money that could be used a sign-on fee for Hayne - remain the favourites to snare the former Parramatta superstar.
Roosters boss John Lee has refused to comment publicly on speculation linking Hayne to Bondi. But leading club officials at the Knights, the Titans and the Dragons have said they would like to have the former representative full-back at their clubs.
Storm football director Frank Ponissi said Melbourne would only be able to sign Hayne "if we got him on a cheap deal".
However Dragons coach Paul McGregor was more forthcoming.
"He's an exceptional talent. I've had a little bit to do with him through Fiji and NSW and we're always after quality players and he is at the top level of that," McGregor told reporters in Wollongong on Tuesday.
"If he was on the market we would like to be in the mix."
The Dragons became the second NRL club after Newcastle to publicly declare their interest in the former Parramatta superstar
"We'll definitely meet with his management and have a discussion," Knights boss Matt Gidley told the Newcastle Herald.
"We can and will look at bringing in a marquee player, if we feel that's going to help our squad."
Chief executive Graham Annesley said the Titans would be "open to discussions" in regard to Hayne.
"Any NRL club would jump at the chance," Annesley said.
Ponissi told SEN radio: "We're always interested in quality players.
"It will be an interesting one if he does come back to rugby league ... you would think he would unless he stayed in rugby union.
"Post this year there's no way in the world we could afford him and the only way we could is if we got him on a cheap deal."
Hayne has previously said he would only return to Parramatta, but whether they could accommodate him under their salary cap for next season remains to be seen.
Parramatta officials have declined to comment on Hayne's probable return to the NRL.