The 24-year-old, who was tipped to be a Premier League star from the age of 18, was released by the Premier League champions in December.
Following his axe, Johnson has since revealed that he suffered from "mental health" issues, which contributed to his career downfall.
"Michael Johnson was a guy with a big talent and I am sad for this, sad for him," BBC Sport quotes Mancini as saying. "He could do everything with his talent. I am very sorry for him. I hope he can resolve all his problems."
Johnson hadn't featured for the North-West outfit since 2009.