The BBC says discussions are underway to extend the Renters Reform Bill to specifically outlaw any rental listing banning families and benefit recipients from applying.
And the talks include having the same approach in Scotland and Wales in addition to England.
At the moment the Renters Reform Bill would, if it became law, apply only to England.
The BBC quotes Westminster government Housing Secretary Michael Gove as saying a joint approach by all three nations would "send a clear message to providers".
A BBC report says: “Mr Gove has written to Scottish Housing Minister Paul McLennan to offer a joint approach. He said talks had also taken place with the Welsh government.”
And it quotes Gove directly, saying: “We know this is a priority we share with the Scottish government, and would send a clear message to providers across the whole of Great Britain.”
A Scottish Government spokesperson is quoted: "We are aware of the UK government's plans to introduce a ban on excluding those in receipt of benefits and those who have children, and welcome this proposal.
"We will work with the UK government as it develops its plans to consider how best to protect these groups in Scotland."
However, the Scottish Government spokesperson adds that any joint approach “must include a close examination of the UK government's decision to freeze Local Housing Allowance rates at 2020 levels for the third year running", saying affordability was "the far more significant barrier to accessing a privately rented home".
A BBC investigation earlier this week found thousands of adverts for rental homes posted by private landlords and letting agents which said children or pets were not welcome.
Almost a quarter of just under 8,000 ads examined on the OpenRent website said families were not allowed to rent the homes, while 300 on Zoopla explicitly said children were not wanted.
You can see the full BBC report here: https://www.bbc.co.uk/news/uk-scotland-scotland-politics-66116194