The American Idol alum acted as a guest judge this week on AGT while Cowell, 60, continued his recovery from back surgery after falling off an electic bicycle over the weekend.
A source told PEOPLE on Monday that the executive producer was in "good spirits" and "walking around again as much as he can."
On Tuesday, Clarkson joked about emulating Cowell's tough reputation in an Instagram video, saying that she would be bringing "country" to the show instead because she has the "worst British accent in the universe."
"It's almost showtime y'all! Getting ready to take over for @SimonCowell! I really need to work on my British accent… 😂😂" she wrote alongside the video. "Looking forward to watching all of the acts!"
In June, Clarkson opened up about the challenges of motherhood, acknowledging that while "overwhelming" at times, there is "no greater gift."
"You are going to be inspired to do all of these magical things with your kids. Do things you've never done before. Try things you've never done before," she said during a virtual ShowHER Love baby shower for new and expectant moms as she teamed up with Carter's. "It is such an awesome experience being a parent. I know it can be overwhelming, but it is so amazing. You aren't just molding their little lives — it's changing you in the process, too."
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