Former Glasgow Rangers manager Smith had a brief spell at the club as assistant to Sir Alex Ferguson in 2004. Fletcher has now revealed that he is keen to see the 63-year-old link up with the Red Devils once again.
"Walter Smith would be a fantastic manager for any club in England, and I mean any club," the Scotland captain told BBC Scotland.
"He still has a lot to give and when Sir Alex eventually retires I would even love to see him at Manchester United. He would be a great replacement.
"Walter is a great manager but I saw the other side of him as an assistant and he was brilliant at that.
"He took some great sessions at training and the Manchester United boys loved him."
Smith left his position as Rangers manager this summer.