The flag was displayed last August, shortly after Gibbs-White's failed move to Tottenham, which resulted in him instead signing a contract extension at the City Ground.
The banner also made lurid and unsubstantiated references to the Greek billionaire's business dealings.
Forest's owner lodged the claim in the High Court last week.
Following an FA investigation into the incident in November, Palace were charged and ultimately fined £50,000, but Sky Sports News understands Mr Marinakis feels that punishment does not mitigate what he considers to be global damage to his reputation, and he is determined to pursue the south London club to the full extent of the law.
Mr Marinakis' case is based on the belief Palace did nothing to prevent the banner being displayed, nor to quickly see to its removal. He is now attempting to ascertain legally how responsible Palace are for the flag being displayed.
Under FA rules, clubs are responsible for ensuring their fans behave in a way which is not "improper, offensive, abusive, insulting and/or provocative".
In defamation cases, there are three areas which can form the basis for a claimant to sue. These include the publication of alleged false statements, creating an image or allowing an image to be displayed.
Sky Sports News has contacted Crystal Palace for comment. Nottingham Forest declined to comment on an ongoing legal matter when approached.
