Hird and Essendon recently lost a Federal Court challenge to the Australian Sports Anti-Doping Authority's investigation of the club.
The court rejected Essendon's assertion that ASADA's probe into the club's 2012 supplement program was unlawful.
Hird, who has served a 12-month AFL suspension, is to return as Essendon's senior coach next season.
But Matthews believes Hird should step away from the Bombers.
"Essendon need a fresh start," Matthews told the Seven Network on Sunday.
"And it's not about Essendon pushing him out. I think James himself ... fresh start. It's not guilt or right or wrong.
"I was supportive of the position as the senior coach 12 months ago but now it needs a fresh start.
"It's Hirdy's choice. I don't necessarily see Essendon pushing him out. You can't put yourself in another man's shoes but that is what I would be doing if I was him."
