The former Tottenham Hotspur boss was the bookmakers' favourite to land the role, but is now said to have told Sky Sports News presenter Jim White that it was "not the right fit" for him.
"I've spoken to Tim Sherwood, who is in Spain at the moment, and he has told me that, after some careful consideration, he no longer wants to be considered as a candidate for the vacant manager's job at Crystal Palace," said White.
"His representative has contacted Palace co-chairman Steve Parish to tell him just that, so Parish now knows that Sherwood has dropped out of the race.
"Sherwood told me, 'I wish them well with the hunt for a new manager, but it is not the right fit for me at this time. Crystal Palace is a great club with a great tradition, but they're in a difficult situation which was unforeseen.'
"Sherwood thanked Parish for granting him an interview last weekend, and he felt the interview went very well, but he no longer wishes to be considered for the job."
Palace are understood to have retracted a job offer made to ex-Cardiff City boss Malky Mackay after his former employers sent a dossier to the Football Association containing allegations of racism, homophobia and sexism.