Former speaker John Bercow's behaviour in public was at times "not acceptable", according to health secretary Matt Hancock.
Mr Bercow continues to face a raft of bullying allegations, which he strenuously denies, with one of his accusers insisting he should not be made a Lord.
Previously, convention has dictated former speakers receive a peerage, though Mr Bercow has not yet been given the honour.
Mr Hancock said he "has never been bullied" by Mr Bercow, though he was aware of accusations.
Commenting on the prospect of a peerage, Mr Hancock told Sky: "I don't think anybody has the automatic right to be a peer."
Pressed on Mr Bercow's actions, he said: "If you look at how he treated some people when he was speaker, like Andrea Leadsom for instance, I think some of the ways that he treated people in public was not acceptable.
"I think in these roles... it's not only important not to bully people, it's important to set an example."
Mr Hancock said that, though convention says Mr Bercow should get one, the former speaker flew in the face of convention "when it suited him".
Earlier today. David Leakey, who served as Black Rod until 2018, stood by his allegations against Mr Bercow.
He told BBC Radio 4's Today programme: "I think that if John Bercow was given a peerage it would be a scandal that Parliament would struggle to live down."
Mr Bercow, who left the role of speaker last year, hit back at the allegations in his latest interview with Sky News on Tuesday.
He told the broadcaster: “Total and utter rubbish – from start to finish."
