It's said that she hasn't left Lamar's side since arriving in Las Vegas last week, following his medical emergency inside a Nevada brothel.
Rumors continue to swirl that the 31-year-old reality star still has "deep feelings" for Lamar.
Following her separation from the former NBA player in December 2013, she moved on with rapper French Montana and eventually hooked up with Harden, a shooting guard for the Houston Rockets, earlier this summer.
What's more, Kardashian and Odom are still technically married; a judge has yet to sign off on their divorce.
In the meantime, Kardashian took to her blog early Tuesday - the first time since she took charge of the situation in Las Vegas.
"The past week has been incredibly difficult. I am so thankful to family, friends and fans, who have sent nothing but prayers and well wishes to Lamar. I also want to take a moment to thank everyone at Sunrise Hospital, including the amazing doctors and nurses for their kindness and diligent work. Under their amazing care, incredible strides have been made. You can never be prepared for an experience like this, but without the outpouring of love and endless prayers that Lamar has received and the strength I was given from my loved ones, it would have been difficult to endure. Thank you for your continued support. God is great!!!"