7:04 AM PT -- 5/14 -- Some good news ... Khabib's father is out of his coma and has regained consciousness after undergoing heart surgery in Moscow, according to reports.
Nurmagomedov family friend Ramazan Rabadanov went on Russian TV and said Abdulmanap has been upgraded to "serious but stable condition" following the procedure.
Abdulmanap is still not speaking -- but the fact he's up and alert is a great sign.
3:27 PM PT -- Conor McGregor is sending positive vibes to Khabib's family ... tweeting out his support and saying he's praying for the Nurmagomedovs.
"Praying for the recovery of Abdulmanap Nurmagomedov," Conor tweeted. "A man responsible for more World champions, across multiple fighting disciplines, than we even know. "
"A true martial genius! Very saddened upon hearing this news tonight."
Khabib Nurmagomedov's father -- who trained the UFC star for most of his life -- is reportedly fighting for this life in a Russian military hospital ... where he's said to be in a medically-induced coma.
Abdulmanap Nurmagomedov is VERY close with his superstar son -- they've traveled together to meet Vladimir Putin on multiple occasions following Khabib's high profile victories in the UFC.