Martial's agent last week said his client will seek a move away from Old Trafford when the transfer window reopens on New Year's Day.
The 26-year-old France international, who joined United from Monaco in 2015, has started only two Premier League games this season and has scored just once.
Martial's representative, Philippe Lamboley, executive director of USFA Management, told Sky Sports News: "Anthony wishes to leave the club in January.
"He just needs to play. He doesn't want to stay in January and I will speak to the club soon."
But Rangnick insisted neither he nor club officials had heard directly from Martial.
"If he has a wish to go to another club, it should be the player who informs either the board or myself," Rangnick said ahead of Tuesday's Premier League match at Brentford.
"I don't communicate with agents via the media and the press. The player hasn't spoken with me or us about it.
"After the final training session before the Crystal Palace game, after having trained with the team, he informed the doctor and medical staff he would not be available because the pain on his knee is too big, so we have to wait and see with Anthony.
"To be honest what his agent says via media is not that much of interest to me."
Martial still has at least three years left on his contract at Old Trafford, having signed a new deal in 2019 that includes an option to extend for a further year.
He has fallen down the pecking order at United, who have an array of attacking talent to choose from, including Cristiano Ronaldo, Edinson Cavani, Marcus Rashford, Jadon Sancho and Mason Greenwood.
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