The education secretary told The Daily Telegraph the measure is set to be dropped under the third stage of England’s roadmap out of lockdown.
Boris Johnson is expected to confirm the change in advice on Monday, according to the newspaper.
When schools fully reopened in early March after lockdown pushed much teaching online, new government advice recommended masks in secondary school classrooms in England to prevent the spread of coronavirus.
Last month, Mr Williamson extended the advice to run until 17 May – but said he expected to scrap it after that.
Since then, unions and scientists have pressed the government to keep masks in secondary school classrooms past this date, telling the education secretary they were “extremely concerned” the measure could be dropped within weeks.
In an open letter earlier this week, education unions, public health experts and parents warned the education secretary such a move would “have consequences for the health” of children, their parents and the wider community.
But Mr Williamson toldThe Telegraph: "As infection rates continue to decline and our vaccination programme rolls out successfully, we plan to remove the requirement for face coverings in the classroom at step three of the road map."
He added: "Removing face masks will hugely improve interactions between teachers and students, while all other school safety measures will remain in place to help keep the virus out of classrooms."
Deaf children told The Independent the measure had been difficult for them, leaving them struggling to understand what classmates with their mouths covered were saying.
Last week, concerns about face coverings disrupting pupils’ learning and wellbeing were raised during the education select committee, during which a Tory MP said she had heard many stories of children “really suffering” from wearing masks.
“Particularly as we’ve entered hay fever season and the pollen can lodge in the mask as the extra heat contributes to children who have skin conditions like teenage acne,” Caroline Johnson added.
In the open letter to Mr Williamson, scientists and unions said face coverings “minimise educational disruption” by allowing students to keep attending school while protecting their families.
The group – which includes members of Independent Sage – said masks help keep those at school safe, allow for wider restrictions to be safely relaxed as soon as possible and are “a critical part of the overall effort to reduce community transmission”.
Their letter added: “To strip these necessary Covid protections, when there are already too few mitigation measures in schools, and when rates of Covid-19 are still significant would have consequences for the health of our children and their parents as well as their communities.”
A Department for Education spokesperson said: "As infection rates continue to decline and our vaccination programme rolls out successfully, we plan to remove the requirement for face coverings in the classroom in line with step three of the road map.
"Virus transmission in schools continues to drop, with the latest data showing a significant decrease in students and staff testing positive and cases isolated quickly thanks to our twice-weekly rapid testing programme."
Additional reporting by Press Association