Is there already trouble in paradise for the newly engaged Johnny Depp and his bride-to-be Amber Heard? Fresh off their winter engagement, the National Enquirer published claims Thursday that the “Pirates of the Caribbean” star is “insecure” over his fiancée’s continuing close bond with her ex-girlfriend, photographer Tasya van Ree.

According to the report, Depp, 50, has been willing to let his 27-year-old bisexual fiancée keep in touch with Ree, 37, her former girlfriend of four years, but has recently become concerned over their relationship. “Johnny has gone out of his way to curb his insecurities since he and Amber started dating,” an "insider" told the gossip magazine, adding that Heard’s recent seven-hour visit with Ree at her Hollywood home and the duo’s multiple phone calls that take place “day and night” have made him worried about their future.

“He’s actually encouraged her to stay friends with Tasya and he gave her full permission to spend time over at her place when she suggested it, but since she came back, Johnny’s noticed how strong Amber’s feelings still are for Tasya,” source the source, adding that Depp has been reconsidering allowing Heard to spend time with her former mate. “He’s having second thoughts about letting her spend time with Tasya again,” added the insider.

Depp and Heard confirmed their engagement in January after three years of dating. The duo, who met on the set of the comedy/drama film “The Rum Diary” in 2011, first sparked engagement rumors after Heard was spotted flashing a diamond ring on her engagement finger while out and about in Los Angeles last month. Two days after the photo of Heard sporting the suspicious sparkler was released, a source confirmed to People that the acting twosome is prepping to tie the knot. “Of course they couldn’t be happier to be engaged and excited to share the rest of their lives together,” a source told to the magazine.

The couple last made headlines earlier this week after Us Weekly published claims that Depp is hoping to have children with his “3 Days to Kill” star belle. “He wants marriage, babies, everything with her,” a source told the magazine, adding that Depp’s two children with French model Vanessa Paradis, Lily-Rose, 14, and Jack, 11, are already smitten with the blonde beauty. “The kids love Amber,” said the insider.