The Equality and Human Rights Commission has recommended that wording in the Equality Act be changed to protect "biological sex" instead of "sex".
The recommendation was made after the government asked the EHRC for advice on re-wording the law.
The EHRC said that the change would "bring legal clarity" to the matter, in particular where it touches on women's sports and single-sex spaces.
The Telegraph quoted an unnamed source close to the Prime Minister as saying that Rishi Sunak was supportive of the revision.
Maya Forstater, whose petition calling for the protection of single-sex spaces was signed by over 100,000 people, prompting a parliamentary debate, welcomed the development as a "huge step forward for common sense".
"The Equality and Human Rights Commission is taking leadership to protect everyone's human rights," she said.
She said it showed the EHRC had "listened to businesses and charities that say they are confused about the law and frightened that they will be sued if they provide a changing room, shower, women's refuge or a sports competition that is female-only".
"We are looking forward to a debate in Parliament on this after Easter. We hope the Government quickly amends the Equality Act to make it clear," she said.
