The 55-year-old's future was called into question at the end of last season after ending his second campaign at Old Trafford without any silverware.
United finished a massive 19 points adrift of Premier League champions Manchester City, whose attacking style of play was in stark contrast to the Red Devils'.
Bosnich believes that his former side have to remain patient, however, using Liverpool, who have gone through numerous managerial changes since last lifting the title in 1990, as a perfect example of how it can go wrong.
"Just stand by him. Give him the opportunity, he is second against a team in Man City who can afford anyone and get anything," he told Omnisport. "Sometimes, even after such dominance, you have got to be patient. You don't want to fall in a situation like Liverpool, after all those years of dominance and then all of a sudden you want to chop and change.
"Stick with this guy, he is a winner and he will bring the glorious times back. People can say what they want. In modern-day football, after we saw the experience with Barcelona, that started with Pep Guardiola, out of something good can come something bad, and vice-versa.
"But, after that, just like after the Leicester thing with chairman saying 'well why can't we do that', we saw a lot of people say 'why can't we play like that?' So, I think a lot of teams suffer for the comparison, that's one of the greatest club sides that anyone has ever seen playing in a way that no one has ever seen before."
Bosnich spent four years at United across two spells, while also representing Chelsea and Aston Villa in the Premier League.