Ronald de Boer this week claimed that his compatriot "was not enjoying the football Manchester United play", while former Holland skipper Ruud Krol remarked to Goal that the 30-year-old "is not settled" at the club.
But Moyes insists he still has a strong working relationship with Van Persie despite United's struggles this season, and denied that the Dutchman was assessing his options.
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"I travelled back from the [Holland] game with Robin the other night. I went to the game, watched them play and travelled back with him. I hardly feel I need to answer the question."
Moyes also refused to chastise Van Persie for comments made after the club's defeat to Olympiakos, when the former Arsenal man said his team-mates made life "difficult" for him, and dismissed any fears of a breakdown in the relationship between the Dutchman and strike partner Wayne Rooney.
When asked if he had issues with Van Persie's remarks, he replied: "None whatsoever, if you actually read the full transcript I understand totally where he was coming from.
"The statistics before they [Van Persie and Rooney] both came back [from injury] proved that we had lost one game with them in the team up until the previous three or four games.
"The record with the two of them in the team was fantastic, so I was talking up how good they were together a month ago. It's only in the last couple of games that has gone.
"We didn't play well at Olympiakos but prior to that we won at Palace and drew at Arsenal. It was that one game that has dragged this up."