Netherlands international Depay, who has a giant lion's head tattooed on his back, organised the photoshoot with the cat while in Dubai where he is undergoing rehabilitation on his knee.
A liger is a cross between a lion and a tiger that is domestically bred and shows traits of both felines.
Two French organizations 30 Millions d'Amis and Code Animal called the photos "unacceptable" and "disastrous" with sources telling ESPN that they would consider legal procedures against Depay.
World Animal Protection Netherlands also slammed the "bad example" set by the Dutch player, asking for the photos to be taken down.
Depay responded to the criticism, by writing: "For those who don't know the facts, shut up.
"The ligers are not even wild animals. They are not born in nature but with humans. I don't think they would survive in the wild."
The groups raised the issue with Lyon, but the Ligue 1 side has decided not to intervene.