Things are getting serious for Kim Kardashian and Pete Davidson. Not only did the comedian get her name branded like livestock, but he is also, “slowly getting to know” her kids. A source told PEOPLE, “He is slowly getting to know her kids. Kim is not pushing it though.”

©Kim Kardashian

The SKIMS founder shares daughters North, 8, and Chicago, 4, and sons Saint, 6, and Psalm, 2½ with ex Kanye West. “She wants to be respectful of Kanye too,” the source said of Davidson meeting the kids.

Kim was declared legally single on March 2 and has been much more open about her relationship with the SNL star since, making it IG official on March 11. “Kim is crazy about Pete. He is spending most of his time in L.A. now,” the source told PEOPLE. “Kim is just very happy and serious with Pete,” the source adds. “Her family loves having him around too. He is very sweet to Kim. Everyone loves seeing her this happy,” they added.

Despite the viral screenshot showing Davidson boasting about being in bed with Kanye’s “wife,” at 8 am, the insider said he doesn’t spend the night at her house. “Pete doesn’t spend the night at her house. Kim wants it to be a comfortable situation for everyone,” they said.

©Kim Kardashian

While Ye hasn’t been posting on Instagram following his 24-hour suspension for bullying, hate speech, and harassment, it’s probably safe to say the rapper won’t be too happy learning Davidson is meeting the kids, even if it’s happening “slowly.”

Before his suspension, Kanye shared a screenshot from a Breitbart article surrounding jokes Davidson reportedly made in 2019, with the caption, “Yet another reason why SKETE gotta stay away from my children.”

He later captioned another Instagram post, “Im [sic] really concerned that SKETE will get my kids mom hooked on drugs. “ “He’s in rehab every 2 months,” he added.

Following the IG posting sprees, the rapper’s performance at the GRAMMY”s was pulled, and a petition is going around trying to get Coachella Music Festival to follow suit.