The couple were plagued with rampant reports recently that their 14-year relationship had come to an end and Depp was also linked to his "Rum Diary" co-star Amber Heard.
But sources claim that the 44-year-old actor is now "trying to work it out" with Paradis, 39, reported E! Online.
"For the first time in a long time, he is talking about her. They both want to make it work," said a source.
Depp has been shooting "The Lone Ranger" in New Mexico and returning to LA most weekends to be with Paradis and their two children - Lily-Rose, 12, and Jack, 10.
The source said that Depp has been "very calm and focused" while filming his role as sidekick Tonto.
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