Kosar, who won the Super Bowl as the backup quarterback with the Dallas Cowboys in 1994, announced the upcoming procedure from his hospital bed on Sunday night, expressing gratitude for the thoughts and prayers received.
The transplant was initially set for the previous weekend but was delayed after the donor's organ was found to be infected.
In the past week, Kosar has undergone five procedures to stop internal bleeding, underscoring the critical nature of his condition.
He was diagnosed with cirrhosis of the liver and Parkinson's disease last year, having experienced liver-related issues for several years.