He is reportedly facing allegations he bet on players he was marking to be the first try scorer while playing for the Tigers last year.
His gambling actions involved a third party, according to the NRL.
Text messages sent by the 25-year-old indicated he knew his behaviour was in breach of the rules, Greenberg said.
"There is nothing more important than the integrity of our game," he said.
"Our fans have a right to expect that every player on every team is doing his best to win each game and we will be relentless in dealing with anyone who attempts to breach this trust.
"At the end of the day, he has deliberately flouted the laws of the game for his own gain and there is no place for him in the NRL."
Greenberg said Simona was remorseful and has been dealing with serious personal issues.
The investigation into Simona's actions, which also involves NSW police, led to him last month being stood down from playing and training.
His rugby league career is in extreme doubt, with England's Rugby Football League indicating the door could be closed on him playing in the Super League.
His prospects of playing in the NRL again would come down to the league's discretion.
Greenberg said the game would continue to offer him welfare services and monitor his well-being.
- AAP
