The recommendation from the Lords Conduct Committee follows an investigation into the Northern Irish peer’s treatment of a parliamentary security officer and MPs Hannah Bardell, Luke Pollard and Toby Perkins.
He was investigated after being “verbally abusive” to security officer Christian Bombolo when asked to show his parliamentary pass in January.
Ms Bardell witnessed the incident with Mr Bombolo.
She complained that when she attempted to intervene she was treated “rudely and aggressively” by Lord Maginnis, who later used “homophobic and derogatory language about her” in comments to the media.
Apprentice Boys of Derry: new era of respect makes for enjoyable ‘Relief’ parade
Feile organisers asked if they have warned Wolfe Tones about leading young people in pro-IRA chants
Thousands expected to take part in 'Derry Day' this weekend
DUP MP calls for probe into Sinn Fein MP’s Twitter post
Brexit: There’s a fundamental con trick being played over Liz Truss’ Northern Ireland Protocol Bill says Lord Empey
Lord Maginnis was also investigated for using homophobic language in relation to Mr Pollard in February 2020 after the Labour MP’s chairing of a meeting.
The Lords Conduct Committee suggested Lord Maginnis’ suspension could be extended if he does not undergo training and change his ways.
In the committee’s report, it said: “In his oral appeal Lord Maginnis showed very little insight into the impact of his behaviour on the complainants, and no remorse for the upset he had caused.
“To the contrary, he portrayed himself as a victim of a conspiracy by people who disapproved of his views and insisted that all his conduct had been provoked.