“Kim is fine with it,” an insider said.

A separate source told us, “Kim is studying and focused on the kids,” referencing North, 7, Saint, 5, Chicago, 3, and Psalm, 2.

West and Shayk, 35, have known each other for years, as she once modeled for his fashion line and starred in his music video for “Power.” They also briefly dated before he hooked up with the “Keeping Up With the Kardashians” star.

He had pursued her a long time ago,” a music-world source told us.

Like many Hollywood relationships, a fashion source said the West-Shayk pairing is beneficial for both of their public profiles.

… He has a stream of projects coming up,” a fashion insider explained.