The former NBA player has been hospitalized since Oct. 13

October 19, 2015 07:35 PM

Although Caitlyn Jenner has not yet visited Lamar Odom in the hospital, she has been keeping a close eye on the former NBA star’s health crisis.

“Caitlyn has been in constant contact with the girls throughout this whole ordeal,” a source close to the family tells PEOPLE.

Members of the Kardashian-Jenner family rushed to Odom’s side after the former NBA player was hospitalized on Oct. 13 after being found unconscious at a Nevada Brothel.

His estranged wife Khloé Kardashian has remained by his bedside. Her entire famous family has visited, with the exception of Rob.

Other friends and family have gathered at the hospital, including Kobe Bryant, Lamar’s father Joe Odom, and Lamar’s two children and their mother.

Odom, 35, has shown signs of improvement, with the star waking up from a four-day coma on Friday and breathing on his own.

“Every day is a little more encouragement, it really has been a miraculous turnaround,” a source told PEOPLE Monday. “He’s not talking. It’s obvious that he understands what is going on because he can nod and shake his head, and he can follow simple commands. He can squeeze the doctor’s hand. He’s still very weak, though.”

Reporting by ELIZABETH LEONARD

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