The debate will provide an opportunity for MPs to question a Government Minister directly on this topic.
More than 109,500 signatories have urged the Government to halt Brexit "if there is no agreement by the deadline for reaching agreement with the EU during the talks".
The petition states: "Leaving with no deal will be very bad for businesses and for the Irish border issue and for EU citizens living here."
The largest number of signatures - 1,094 - has come from the Northern Irish constituency of Foyle, represented by Sinn Fein MP Elisha McCallion.
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The second biggest group (667 signatures) was from Labour MP Thangam Debbonaire's Bristol West constituency and the third largest of 650 from Labour MP Daniel Zeichner's Cambridge constituency.
The debate by MPs on the Petitions Committee will start the debate in Westminster Hall at 4.30pm and will be opened by Labour MP Liz Twist.
In response to the petition, a Government spokesman said: "Whilst striking a deal with our EU partners remains the outcome we expect, no deal plans are well-developed and we stand ready to make a success of Brexit, whatever the outcome of our negotiations.
"We are leaving the EU. That's what the British public voted for and that is what we will deliver."