Walliams is one of the UK’s most successful children’s authors, having sold more than 60 million copies worldwide in 55 languages.
HarperCollins published his first children’s book, The Boy in the Dress, in 2008.
Some of his books, including Gangsta Granny and Billionaire Boy, have also been adapted into television films.
He has published more than 40 books in total, including a Christmas book titled Santa & Son, which was published by HarperCollins in October.
Two of his books – Mr Stink and The Boy in the Dress – have been adapted into TV films, which were shown on CBBC on Sunday.
Walliams is also scheduled to appear on comedy panel show Would I Lie to You? on Boxing Day on BBC One.
A spokesperson for the BBC said on Friday: “While we’re not making any changes to the festive schedules, we have no future projects directly involving David Walliams.”
A spokesperson for Walliams said he had “never been informed of any allegations raised against him” by his publisher.
“He was not party to any investigation or given any opportunity to answer questions. David strongly denies that he has behaved inappropriately and is taking legal advice,” the spokesperson added.
The publisher said it took employee wellbeing “extremely seriously” with “processes in place for reporting and investigating concerns”.
“To respect the privacy of individuals we do not comment on internal matters,” the company said.