Liz Johnstone, 59, stayed Drumchapel Road, where she brought her two children up, for over 30 years.
McAvoy often made time to visit Liz in the North Glasgow housing estate.
Liz, whose daughter Joy is also in the acting industry, battled ill health for many years before passing away last month.
Police Scotland said in a statement: "The body of a 59-year-old woman was found in a a property on Drumchapel Road on January 18.
"The death is being treated as non-suspicious and a report will be sent to the Procurator Fiscal."