Parliament will meet on 19 October after a crunch EU summit – seen as the last chance for the UK and EU to agree a deal ahead of 31 October deadline.
If a deal is agreed, Boris Johnson will ask MPs to approve it – but if not, a range of options could be presented.
The BBC’s Laura Kuenssberg says these could include leaving without a deal, and halting Brexit altogether.
MPs will have to agree a business motion in the Commons for the sitting to take place.
If agreed, the additional day would coincide with an anti-Brexit march run by the People’s Vote campaign, which could see thousands of protesters heading to Westminster.
The House of Commons has only sat on four Saturdays since 1939, including on 2 September that year, due to the outbreak of World War Two.
The last time there was a Saturday sitting was 3 April 1982, due to the invasion of the Falkland Islands.