United fanzine Red Issue published reports that a senior player had "ripped into" the under-fire Scotsman, who has failed to keep the club's Premier League title bid alive after replacing Sir Alex Ferguson last summer.
Reports have claimed that the player in question clashed with the Scotsman with regards to his training methods.
According to the Daily Star, Giggs, who was appointed a player-coach when Moyes arrived at Old Trafford, has described the rumours as 'total and utter rubbish'.
There is increasing pressure on the former Everton boss, who witnessed the Red Devils succumb to a 3-0 defeat at the hands of arch rivals Liverpool on Sunday.
United are seventh in the league table, 12 points off a Champions League place and 18 points below leaders Chelsea.