The agency, which works with MI6 and MI5, was dragged into the scandal following claims made on Thursday by Trump’s press secretary Sean Spicer.
Without providing evidence, Trump has accused his predecessor of bugging his hotel during last year’s elections.
Trump finds himself increasingly alone in his claims of being spied on but Spicer says he stands by the allegations.
“He didn’t use the NSA, CIA, the FBI or Department of Justice – he used GCHQ.”
But GCHQ says such claims are utterly ridiculous.
In Britain, concerns are now being raised about the damage these claims may do at an intelligence-sharing level.