On Sunday Steven Naismith and Steven Whittaker both announced their objections to transferring their contracts to newco Rangers and confirmed they will not report back to Murray Park for training this week and consider themselves free to find new clubs.
Green responded by reiterating previous warnings that he will challenge any attempts by players to walk away from his club for nothing.
He said in a statement: "It is a great pity that certain players have chosen this time to attempt to tear up their contracts and walk away from the club."
The statement continued: "The club is facing massive challenges in terms of its league status and the last thing the fans want to see is a dispute between the club and players.
"However, it appears that is the route several players are choosing. I can assure those players and clubs who may be interested in signing them that Rangers will seek damages for breach of contract and for inducement to break contracts."
Green's Sevco consortium completed the purchase of the business and assets of Rangers for £5.5million after failure to secure a Company Voluntary Arrangement (CVA) to exit administration consigned the club to liquidation.
His new company now faces a battle to play in the Scottish Premier League next season, with all 12 clubs set to vote on the issue on July 4, with Hearts and Dundee United having already indicated they will reject Rangers' bid.
Both Naismith and Whittaker cited concerns over their careers if forced to drop down the divisions as a contributing factor when making the decision to object to transferring their contracts to the newco.
However, Green confirmed Rangers have informed the Scottish Football Association today of their intention to challenge those actions.
He added: "The SFA has been considering the issue and has issued a preliminary guidance note on registration issues. That note has made it clear that it is open to the club to challenge the actions of the players."