According to the source, the split "was a long time coming."
"They have had issues for a couple
years, but always worked through them for [son] Kiyan," the source says, adding that the breakup is "amicable and they have much respect for one another."
A source close to the couple tells ET "no divorce papers have been filed and as of right now, this is just a separation. No one knows what will happen in the future but there are no plans to move Kiyan out of New York City and nothing will change for him."
As for reports that the New York Knicks player allegedly got a stripper pregnant, two sources tell ET that the baby rumors are false. "Carmelo has told La La and those close to him that these rumors about him impregnating a dancer are not true," one source close to the couple tells ET.
Meanwhile, TMZ reports that La La moved out of the family home last week, and is currently living in her own place in New York City. According to the report, the two have had "ups and downs" in the past, but Carmelo's current season with the New York Knicks has been "extremely stressful" on the marriage for the past few months.
Carmelo, 32, and La La, 37, have one child together, 10-year-old son Kiyan, and were married in July 2010 after getting engaged on Dec. 25, 2004.
Last month, La La posted a sweet photo of Carmelo and Kiyan snuggling on the couch.
In February, Carmelo also wished La La a happy Valentine's Day.
Last October, La La was one of the first to visit
her good friend, Kim Kardashian West, in New York City after the reality star was robbed at gunpoint in Paris, France.
-- Reporting by Jennifer Peros