Some peers want the US president to address MPs and members of the House of Lords in Parliament’s Royal Gallery during his planned visit to Britain.
Conservative Lord Cormack said Mr Trump should be given the opportunity to speak to both Houses and be received “with proper good manners”.
Lord Speaker Lord Fowler said there had been no conversations with the UK Government about a possible address by the president, but “any request for him to be speak in the Royal Gallery would be discussed if and when it were received”.
He noted the “United States is a long-standing ally and friend of the United Kingdom”.
The Independent reported that peers were pushing for the president to speak in the Royal Gallery, a lavishly decorated room at the House of Lords end of the Palace of Westminster where Mr Bercow’s opposition would carry less weight.
Both Ronald Reagan and Bill Clinton addressed peers and MPs in the Royal Gallery during visits to the UK.
Former MP Lord Cormack told the website: “He is the president of the United States, our most important ally.
“My own personal views on him are completely irrelevant. We should give him the opportunity to speak to both Houses.”
He added: “He should be received with proper good manners and as far as a speech is concerned ... he would speak where most other presidents have spoken – in the Royal Gallery.”
Mr Trump will make a working visit to the UK on 13 July and details of his trip have yet to be confirmed.
The US ambassador to Britain, Woody Johnson, said Mr Trump “really wants” to meet the Queen, adding the president would “definitely” be coming to London despite the warnings of likely demonstrations.
Former trade minister Lord Jones of Birmingham said it would be an “excellent idea” for Mr Trump to speak in Parliament.
“Trump is the democratically elected leader of our largest trading partner, our biggest inward investor and the guarantor, when all’s said and done, of our security,” he said.
“The bosses of China and Saudi Arabia are happily invited.”
Mr Bercow said in February last year he was “strongly opposed” to Mr Trump addressing both Houses of Parliament in Westminster Hall, as predecessor Barack Obama had done.
But Lord Fowler was not consulted and told peers at the time he would “keep an open mind and consider any request for Mr Trump to address Parliament, if and when it is made”.
Tory former Cabinet minister Lord Tebbit said there would be support from “a lot of peers” if Lord Fowler offered to host a speech by the US president.
“John Bercow took a unilateral decision,” Lord Tebbit said. “I am not sure he has the power to.”
Lord Fowler pointed out that since becoming Lord Speaker the king of Spain and president of Colombia had spoken in the Royal Gallery - the use of which had been approved by him and Lords official Black Rod, rather than Mr Bercow.
He added: “No conversations have taken place between the House of Lords and the UK Government regarding President Trump coming to the Royal Gallery.
“Any request for him to speak in the Royal Gallery would be discussed if and when it were received.
“The United States is a long-standing ally and friend of the United Kingdom.”