Kim Kardashian Is 'Trying to Be Respectful' of Kanye West But Has 'Moved On,' Says Source

Kanye West has made a series of public pleas to reunite with Kim Kardashian 

Kim Kardashian West is continuing to focus on her co-parenting relationship with ex Kanye West amid the rapper's public pleas for her to get back together with him.

While performing at the Free Larry Hoover concert Thursday at the Los Angeles Coliseum, West, 44, dedicated his song "Runaway" to Kardashian West, 41.

After singing the lyrics, "I need you to run right back to me, baby," he added, "more specifically, Kimberly." The move was the latest in a series of statements he has made about wanting to reunite his family.

A source tells PEOPLE that Kardashian West "knows where Kanye's head is" but "ignores it."

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The source says Kardashian West "has moved on" but "she knows it's difficult for Kanye to deal with." Says the insider: "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."

Kim Kardashian and Kanye West. Frazer Harrison/Getty

Kardashian West attended the Thursday concert with her sister, Kendall Jenner, and her mom, Kris Jenner. She also brought along two of her children with West: North, 8, and Saint, 6. The former couple are also parents to daughter Chicago, 3½, and son Psalm, 2½.

The source says that eldest child North "is especially a fan of her dad's music" and Kardashian West wants to make sure her kids have access to their dad and his events.

"Kim will always bring the kids to events that are important to Kanye," the source adds. "Co-parenting and making sure her kids are happy will always be her priority."

Kardashian West filed for divorce from West in February after nearly seven years of marriage. The duo began dating in 2012 and later wed in 2014.

Kim Kardashian and Kanye West. Pierre Suu/Getty

The SKIMS founder has recently been dating Saturday Night Live comedian Pete Davidson, whom she's been linked to since they were photographed holding hands at Knott's Scary Farm in Buena Park, California in October.

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A source told PEOPLE last month that Davidson is "exactly" what Kardashian West needed amid her divorce from West.

"He's exactly what Kim needed after her divorce — someone to make her laugh and just have a fun time with," the insider said. "The end of her marriage was a very dark time for her and Pete has been the best antidote."

"They have been getting to know each other quickly," the source added. "Kim likes him more and more."