The 46-year-old was admitted to hospital for brain surgery earlier this month after collapsing at his home in the north of England.
Posting on Twitter, McNamara's daughter Erin said: "Thank you for the continued support for my dad, the past week has been so overwhelming for us as a family.
"He is making progress but still has a long road to recovery.
"We are so thankful for all the care he's received and remain positive."
McNamara began his senior career with Dunfermline Athletic and went onto play more than 350 games for Celtic. Shorter spells followed at Wolves, Aberdeen, Falkirk and Partick Thistle before he took on management duties at the Jags and later Dundee United and York City. He also served as the Minstermen's chief executive until March 2018.
He was capped 33 times by Scotland. Recently he had been working as an agent as well as advising Dunfermline through his sports management firm. He also recently opened a sports bar in Fuengirola in Spain, with long-time friend and former team-mate Simon Donnelly.