The news comes as West has made several public comments about his intentions to try and win Kim back.
Earlier this week, the music mogul dedicated his song "Runaway" to the SKIMS founder while performing at the Free Larry Hoover concert at the Los Angeles Coliseum.
After singing the lyrics, "I need you to run right back to me, baby," he added: "More specifically, Kimberly."
But sources said after the concert that Kardashian – who is reportedly romancing Pete Davidson – has "moved on" from West and as no interest in rekindling their romance.
An insider said: "[Kim] knows where Kanye's head is, but she ignores it. "[She has] moved on but she knows it's difficult for Kanye to deal with.
She isn't surprised that he pleads in public for her to run back to him. She is just trying to be respectful about it."
Kardashian is determined to keep her relationship with West civil, and insiders say she is particularly invested in ensuring they remain good co-parents to their children - North, 8, and Saint, 6, Chicago, 3, and Psalm, 2.
The source added: "Kim will always bring the kids to events that are important to Kanye. Co-parenting and making sure her kids are happy will always be her priority."