Giggs had been touted as a possible replacement for the late Gary Speed, who took his own life last year.
However, an offer of a part-time role for the 38-year-old was rejected by Ferguson, according to The Mirror.
"[Giggs] was always seen as the natural successor to Gary, but Sir Alex immediately told us there is no chance," a Wales source is quoted as saying.
"It's disappointing as many saw Ryan as the man to continue the foundations laid by Gary. But even a part-time role, which was also mentioned, was also immediately rejected."
A six-man panel has been appointed to find a successor for Speed before Wales take on Costa Rica on February 29.