The National Enquirer claims the monarch favours William and is "secretly grooming him to take over."
According to a new biography, Charles At Seventy: Thoughts, Hopes and Dreams, a palace insider explosively dished: "William has total respect for the Queen."
However, other sources noted William and Harry haven't always shown "proper respect" to their father Charles.
Even though the Prince of Wales has assumed many of the monarch's responsibilities, palace sources said Elizabeth will only allow Charles to operate as a shadow King.
That news counters claims in the book by Robert Jobson, which stated, "Some close to the monarch say if she reaches 95...she will officially transfer all executive powers to him, as Prince Regent.
Other sources insisted the concerned Queen thinks Charles is "unfit to rule."
The Royal Family has not responded to the National Enquirer's report.