Johnny Depp to Tie the Knot?

Is Johnny Depp finally making an honest woman out of his long-term girlfriend, Vanessa Paradis?

Though the Pirates of the Caribbean star has said, “I don’t feel like I need a piece of paper that says I own her and she owns me, ” the 45-year-old may have had a change of heart.

Sources tell OK! that the actor had a high-end Southern California jewelry store shut down so he could privately shop for engagement rings on Dec. 10 for Vanessa, mom to his children, Lily Rose, 9, and Jack, 5 – and that he made a “very large purchase.”

“This was Johnny’s third or fourth visit to the store,” a source tells OK!. He looked at an assortment of classic solitaire diamond rings in platinum settings – a really beautiful selection of elegant and understated rings.”

Johnny, who met Vanessa in 1998 while filming The Ninth Gate, praises the French singer for giving him “proper perspective and understanding” after failed engagements

to Winona Ryder, Sherilyn Fenn and Jennifer Grey, and a tumultuous relationship with supermodel Kate Moss.

“We just have a miraculous understanding of each other,” he's said.