Hayne left the Eels in October 2014 to chase his NFL dream."We have always made it very clear that we would love to see him back," Greenberg told Fairfax Media.
"I actually sat with Jarryd in round one at Pirtek Stadium this year and told him we would welcome him back. That has only strengthened on today's news.
"So, if and when Jarryd is prepared to make the decision on the next stage of his career, if he wants to have a discussion with us about the NRL, we are more than happy to have that discussion."
However Greenberg ruled out using the NRL's much-vaunted war chest to tempt Hayne back to the NRL, NSW skipper Paul Gallen and Hayne combined for the Blues drought-breaking series win in 2014 and Gallen, who plays his last game for NSW on Wednesday also said he would welcome the superstar fullback's return.
"I think everyone would like to see him back," Gallen said.
"He's a drawcard. I just spoke a minute ago about drawing kids to the game and he does that."He missed out there, it would have been a pretty good thing to go to the Olympic Games but it wasn't to be for him and certainly I'd love to see him back in the NRL."
Hayne announced on Facebook on Monday he has missed selection in Fiji's Olympic team.
"I used all my experience as a professional athlete and have tried every day and in every way possible to make this team and make it better, but unfortunately, time has been against me," Hayne wrote.
Kieran Foran's exit from the Eels would free up funds for Hayne to return to the Eels.
Parramatta were hit with a $1 million fine and the loss of 12 competition points last week as the NRL made its final decision on the Eels' salary cap irregularities.
- AAP