Lord Lisvane, who was Clerk of the House, has handed a dossier of allegations to the Parliamentary Commissioner for Standards, according to The Times.
Mr Bercow, who has previously denied claims he bullied members of his staff, dismissed the new claims as having come at a "curious" time, with suggestions that he may be in line for a peerage.
The document is said to accuse Mr Bercow – who is reportedly being lined up for a peerage by Labour leader Jeremy Corbyn – of having bullied and humiliated staff, including using inappropriate language.
In a statement on Thursday, he said: "During the five years that we worked together, Lord Lisvane had ample opportunity to raise any accusations of bullying with me.
"At no stage did he do so, even though he became Clerk of the House - the most senior official. The timing of this intervention is curious.”
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Commenting on the claims, business secretary Andrea Leadsom has said that if a complaint of bullying by Mr Bercow is upheld, it should have an "impact" on whether he is made a peer.
Mrs Leadsom, who as leader of the Commons clashed repeatedly with Mr Bercow, said that the complaints procedures for Commons staff which she helped establish, applied to everyone in the House.
She told Sky News: ”The whole purpose of that was that anybody, including the speaker of the House of Commons whoever he or she may be, should also be subject to that procedure.
"In the event that there are genuine, upheld complaints about any persons that should have an impact on whether they are found suitable for the House of Lords.”
There have been suggestions that Downing Street could hamper the move to make Mr Bercow a lord, with the prime minister's official spokesman highlighting a "long-standing convention" that opposition leaders nominate individuals form their own parties.
Mr Bercow left the speaker's chair on 31 October and has been replaced by Sir Lindsay Hoyle.