40-year-old Giggs, United's most decorated player, was left out of the squad for Sunday's miserable 3-0 defeat to Liverpool.
On Monday, rumours of a rift began to surface with some claims even suggesting the two clashed after the match.
However, the club have been quick to deny there is any problem at all between Moyes and the veteran Welsh midfielder.
A club spokesman is quoted by the Sun as saying: "The story of any problems between Ryan and the manager are completely false."
Giggs, who is under contract as a player, was appointed to United's coaching staff by Moyes in the summer.