Reports on Thursday suggested that several peers were pushing for him to get the chance to make a speech in the Royal Gallery when he makes the trip on 13 July, or during a later state visit.
Mr Trump had been barred from the House of Commons by Speaker John Bercow ahead of a presumed state visit last year, citing an “opposition to racism and to sexism and our support for equality before the law”.
But Mr Bercow – who is facing calls to resign over accusations of bullying – has no direct control over the Royal Gallery, which was addressed by Ronald Reagan in 1982 and in 2017 by Chinese President Xi Jinping.
Peers including Lord Cormack and Lord Tebbit are said to be among those keen for the Speaker, Lord Fowler, to extend his own invite to Mr Trump to Westminster.
Speaking in the Lords after Mr Bercow’s declaration last February, Lord Fowler said he would “keep an open mind” as to whether to invite Mr Trump.
Addressing Thursday’s reports, Lord Fowler said “no conversations had taken place” with the Government about the possibility but any request “would be discussed if and when it were received”.
“Since becoming Lord Speaker in 2016 I have welcomed both the King of Spain and the President of Colombia to Parliament,” he said.
“Both addressed members of the House of Commons and the House of Lords in the Royal Gallery, the use of which was approved by myself together with Black Rod.
“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 US is a long-standing ally and friend of the United Kingdom.”
During his working visit to the UK, Mr Trump will hold talks with Prime Minister Theresa May and could also meet the Queen.
The Telegraph reported last month that the visit will be held predominantly outside London, amid fear of protests.
The newspaper said Mr Trump would stay overnight and hold talks with Mrs May at her countryside retreat of Chequers.
The trip is being held ahead of a NATO summit.