Hugh Baird, 40, was found dead in his cell at Barlinnie Prison on Monday. The death is not being treated as suspicious.
Baird, from Glasgow, was due to stand trial next week over the murder of Jennifer, 33, in Alexander Place, Kirkintilloch, on April 18 this year.
He was accused of sitting outside Ms Morgan’s house in a car and shouting at her when she appeared before following her and repeatedly stabbing her.
Police Scotland confirmed they received the report of Baird’s death at Barlinnie at around 7.05am on Monday.
The spokesperson stated: “The death is not being treated as suspicious.”
A Crown Office spokesman added: “The Procurator Fiscal has received a report in connection with the death of a 40-year-old man in Glasgow on October 8, 2018.
“The investigation into the death, under the direction of Scottish Fatalities Investigation Unit (SFIU), is ongoing and the family will be kept updated in relation to any significant developments.”