The speculation, which has not been proven, recently surfaced on the social networking site and was given as one of the reasons as to why the England international is yet to turn out for the Red Devils this season.
However, while Zaha opted not to reveal what he was responding to, he posted this afternoon: "Silly rumours #childish."
Although no indication has been given by the player, it has since been claimed that he was keen to put an end to the allegations.
Zaha featured heavily during United's pre-season tour of the Far East and Australia, but since the Community Shield against Wigan Athletic in August, he has rarely been in Moyes's plans over recent weeks.
However, he did score for the club's Under-21 side last night.