The 46-year-old's condition was described as "critical but stable" by Hull Royal Infirmary earlier today, but The Sun are now reporting that the former footballer is now communicating with family and medical staff.
Worried former team mate at Celtic John Hartson tweeted to say that Jackie had "collapsed at home Saturday with a bleed on the brain", before adding that his "thoughts are with his wife Samantha and the children."
Former Partick Thistle and Dundee United manager McNamara left his role as chief executive of York City in March 2018, but it is understood that he still has a home in the city.
McNamara's family wrote on Twitter that he was receiving the "best care possible".
A post on McNamara's personal Twitter account read: "This is Jackie's daughter. Thank you all for your kind words and support. My dad is getting the best care possible, as you all can understand this is difficult for us as a family and request privacy at this time."
Other former clubs including Aberdeen, Wolves and Dundee United also sent their best wishes.
The former York manager has been working as a players' agent as well as advising Dunfermline through his sports management firm.
McNamara recently opened a sports bar in Fuengirola, Spain, with Simon Donnelly, his former Celtic team-mate and managerial assistant and close friend.