The petition has so far secured more than 128,000 signatures and calls for the 31 March deadline to be extended to avoid people being caught out through no fault of their own.
Financial secretary to the Treasury Jesse Norman MP will respond to the proposal although the government has already said it will not be extending the period.
This is despite warnings from the conveyancing industry that completions are becoming a lottery and fears that around 100,000 deals may not make the deadline.
The 90-minute virtual session will be open to MPs, including those who are self-isolating or shielding, and will be broadcast live on parliamentlive.tv and YouTube.
The session is a special sitting of the Petitions Committee of MPs, rather than the typical Westminster Hall setting as this is closed due to the Covid-19 pandemic and the government has refused to allow virtual debates in its place.
The Commons Petitions Committee which schedules petition-related debates also granted a session for the petition relating to arrangements for UK Musicians in the EU which raised 280,000 signatures.
Catherine McKinnell MP, chairwoman of the committee, said: “I’m delighted we have been able to schedule two e-petition sessions, where members from across the House, including those self-isolating and shielding, will be able to scrutinise the government directly on issues raised by petitioners.
“As was the case when Westminster Hall was closed due to Covid-19 last year, we have had to innovate to find ways to hold the government to account, and crucially to voice the concerns of petitioners in the House of Commons, while our usual debates cannot be held.
“As these petitions demonstrate, there are important issues affecting hundreds of thousands of people that are being missed. Their calls for help and support must be heard.”