The former Olympian, 71, recently appeared on the Full Send podcast and gave her opinions on Kardashian's new boyfriend after meeting the Saturday Night Live star for the first time.
"He was over the other day," Jenner said of Davidson, 28, on the show. "I met him for the first time. I was in trouble because I called him Peter and Kimi now starts laughing, 'It's not Peter, it's Pete.' I said, 'I don't know. I'm just trying to be, you know, polite,' you know?"
"He seems like a very nice guy but the best part was, Kim seemed, honestly, Kim seemed so happy and that's my number one concern, is her happiness," she added.
Davidson and Kardashian, 41, were first romantically linked last October after they were spotted holding hands on a rollercoaster at Knott's Scary Farm in Buena Park, California. They also shared an onscreen kiss that same month on SNL when she Kardashian made her hosting debut.
Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.
In February, Davidson called Kardashian his "girlfriend" for the first time in an interview with PEOPLE (The TV Show!) host Kay Adams. Then in March, the Keeping Up with the Kardashians alum finally made their relationship Instagram official shortly after being declared legally single amid her divorce from Kanye West.
Their divorce turned contentious in recent months, with West, 44, bringing their children into the dispute. He also faced controversy over his recent "Eazy" music video, which depicted him kidnapping, tying up and burying a claymation Davidson alive.
ANGELA WEISS/AFP via Getty; Stefanie Keenan/Getty; John Shearer/Getty Images
Despite recent drama, Jenner admitted on the podcast that she was a fan of Kardashian and West's relationship and is still "good friends" with the rapper.
"I really like Kanye," she said. "Every time we've been together he's been absolutely great, especially during the transition and this and that. He was absolutely phenomenal. I'm still, today, when I see him, we're good friends. I just have to be a little careful because you know, he says some things, especially towards the family. Obviously I'm on the family's side. I wish him nothing but the best. I'd love to see him again."
Getty (3) Kanye West; Kim Kardashian; Pete Davidson
Since the SKIMS mogul has moved on, a source told PEOPLE earlier this week that Davidson has been spending a lot of time with her and bonding with her family.
"Pete fits right in with Kim's family," the insider shared. "They all love him."
"He is slowly getting to know her kids. Kim is not pushing it though," the source shared. "Pete doesn't spend the night at her house. Kim wants it to be a comfortable situation for everyone."
Kardashian also spoke about her ongoing divorce in a conversation with Robin Roberts on Wednesday night.
"You want to take the high road and sometimes it's hard," she said on the ABC special. "I've always been a champion of him speaking his truth."
Kim Kardashian/Instagram Kim Kardashian West and Kanye West with kids North, Saint, Chicago and Psalm
When it comes to their four children, Kardashian said she is "really open and honest with them" about their split.
While Kardashian acknowledged that her "younger ones don't really understand," she noted that their older two kids "know what's going on."
"You have to just be there for them," she said. "No matter what, even in this crazy life that we live, you just have to have a really open dialogue with your children. Kanye and I have had conversations. We have to talk daily for the kids so you know, I hate that it had to play out like that. But when it comes to family, I mean, Kanye and I will always be family."
"At the end of the day, I just want my kids to be happy and healthy, and think the world of their dad," she added. "And they do."