The couple, who have two kids together, announced last month they had "amicably separated", reported Sun online.
But it is said that Depp has flown to Paradis in the South of France to try to patch up their relationship.
The "Pirates of the Caribbean" star gave the model an antique gold pendant bearing the message "My heart is always with you."
"He presented her with such a touching gift, it's almost as if they could make another go of things. Johnny wants to be with his family, he's a very family orientated man. His kids mean everything to him.
"What they need more than anything is to get together far away from Hollywood and that is what they are doing," a source said.
Earlier reports said that Depp and his "Rum Diary" co-star Amber Heard, 26, had grown very close on set, which prompted Depp to separate from Paradis.
