Carmelo and La La Anthony have been living separately, sources say, but friends close to the Knick’s wife say she’ll stand by her man and won’t split from the NBA star.

“It is true they haven’t seen much of each other in the past few months,” says a friend of the couple. “She’s been away a lot filming her show, ‘La La’s Full Court Life,’ in London, New York and LA. They are not separated and are still together. She and Melo have a house in LA — so she’s always there when she’s doing auditions.”

But others say they’ve been going through a more rocky period. “They have been living separately for several months now,” says a source. “She’s been living in LA while Carmelo has been in New York.” The source added, “La La used to go out to the games and wanted to be seen . . . now she’s always off doing her own thing.”

Sources add that La La’s also been partying with girlfriends from Mexico to Miami, which has displeased Melo and “made him angry.”

According to multiple sources, the pair had been seeking a new home over the summer and were checking out apartments in TriBeCa for up to $25,000 a month. But the search cooled along with the relationship. “During the summer they were looking for a new apartment constantly,” said a source. “About two months ago, that completely dried up. They don’t even return their brokers’ phone calls anymore.”

After Melo was set off by the Celtics’ Kevin Garnett for allegedly saying La La “tastes like Honey Nut Cheerios,” speculation over infidelity flew. But sources insist that’s not the root of the couple’s split. “I have not heard anything about him having another woman,” said one pal, adding, “La La has never slept with Garnett.”

Melo was suspended for one game for the post-game clash with Garnett over the incident.

Reps for Carmelo and La La Anthony declined to comment. But reached by The Post at the home of La La’s mother in Stone Mountain, Ga., a relative named Paul Fryson said of the Cheerios dig: “I’ve heard it. It is very serious . . . We’ll handle it.”