The pair were dating for over a year before the France defender, 32, gave the ex-Baywatch beauty a promise ring after helping his nation to glory in Russia.
TMZ claim they discussed marriage, but 51-year-old Anderson decided against it.
Now the American is preparing to move out of her and the Marseille star’s home in the French Riviera.
The report also claims the Cartier ring Rami gave her has been passed to her eldest son Brandon.
Anderson, who is set to appear on France’s version of Dancing With The Stars, reportedly feels she is a barrier to the footballer seeing his two sons.
Page Six claims a source told them: “After spending this past week with Adil’s cute twin sons… it broke Pam’s heart that he doesn’t see them enough, as he should, so she’s moving out.
“Pamela feels she is the reason Adil doesn’t spend enough time with his children.
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She is removing herself from his life so he can do the right thing and be with his kids.
"It’s a selfless move by Pamela, a true romantic — and she is heartbroken.
“Adil has difficulty balancing his life with Pamela and what should be a healthy relationship with his ex, the mother of his children.”
It also states Anderson is hoping Rami will reunite with the mother of his kids.
The former Milan and Sevilla ace was an unused substitute for his country in their goalless draw with Germany on Thursday.
He was part of France’s World Cup squad that claimed glory this summer but failed to play a single minute in Russia.
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