Commons Leader Jacob Rees-Mogg has tabled a motion for the House of Commons to rise on Wednesday until April 21.
The move would see MPs break from their duties in Westminster almost a week early - the initial recess date for Easter had been set for Tuesday, March 31.
It comes after Prime Minister Boris Johnson urged people to stay in their homes unless "absolutely necessary" in a bid to prevent the further spread of Covid-19.
MPs have been following party guidance on attending debates in a bid to limit those in the Chamber at any one time.
The Coronavirus Bill is expected to receive Royal Assent and become law before the end of Wednesday.
MPs from all sides agreed to let it pass without formal votes.
Communities Secretary Robert Jenrick said he was "certain" MPs would return after the Easter recess to review whether Parliament should reopen during the pandemic.
The Cabinet minister told BBC Breakfast: "Once that's happened [the passing of the Coronavirus Bill] then it may be a sensible thing to close Parliament down for the recess and then review that at the end of the recess after Easter.
"Most of us, I think, do want Parliament to continue.
"We live in a democracy, it' essential there's scrutiny of the steps that the Government is taking."
He added: "But obviously Parliament has to lead by example, follow the guidelines wherever it can, and ensure that we protect the staff that work in Parliament as well."
Mr Jenrick said he was unaware of whether Mr Rees-Mogg would call for a fixed return date.
He added it was his opinion that Parliament should return in "some form" after recess.
Mr Jenrick told the BBC: “I think it’s really important, however deep and serious this crisis, that Parliament in some form continues to operate because you as citizens want to ensure your MPs are holding the Government to account.”
He stressed, however, that technical teams were under strain due to staff shortages related to the coronavirus outbreak.
It is not known whether the Speaker would consider allowing MPs to hold Commons debates via video conference.
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