The Mirror says Young has been castigated for going to ground theatrically to earn a penalty in the Reds' Champions League draw away to Real Sociedad on Tuesday.
Although Moyes refused to publicly condemn Young in the immediate aftermath of the incident, it is understood the Scot was going to have a quiet word.
Young, 28, was told off by Moyes in September after being booked for taking a dive in a 2-0 win over Crystal Palace at Old Trafford.
His propensity for diving has given Moyes a fresh headache and created a culture of mistrust around the player.
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