If any of them sign elsewhere, they face the prospect of playing out the 2020 season at their current club before moving.
“I think it’s in the best interests of the game, particularly the fans to try to tidy it up a bit,” Greenberg said.
“I don’t like the ability of such a long-term outcome for players to announce that they’re playing at another team.
“So I think there’s merit in having a discussion about bringing a more orderly process to transfer windows and contracting periods.”
Greenberg remains in drawn-out negotiations with the Rugby League Players Association, who have so far rejected the option.
A proposed model put forward by the NRL this year featured a mid-season transfer window near the representative period as well as in parts of the off-season where players could immediately swap clubs.
The plan also aimed to monetise the process, offering financial benefits for players.
However, the RLPA has rejected changes it believes might restrict player-movement rights enshrined in the current collective bargaining agreement.
“I understand their position, too … it’s a negotiation like a lot of things in the game,” Greenberg said.
“I haven’t given up on that though
“Whether that falls into this year or it goes into the next Collective Bargaining Agreement [in 2023] I’m not sure.
“But I think there’s great merit. I’ve said that openly a number of times and it’s got strong support from the clubs as well.”
Meanwhile, the futures of several other players still contracted longer-term are also clouded headed into next month, as clubs prepare to return to training.
Want-away Wests Tiger Ryan Matterson has been given permission to test the market and seems almost certain to be elsewhere next year.
Matt Moylan is reportedly also a possibility to leave Cronulla, with the Sharks needing to manage their salary cap to welcome Jesse Ramien back to the club.