Ministers believe MPs will reject the two changes made to the Brexit bill in the House of Lords when they debate it for the second time later.
Peers want to guarantee the rights of EU citizens in the UK and ensure Parliament has a vote on any deal.
The EU Withdrawal Bill could complete its final stages if both Houses of Parliament agree the text of the bill.
PM Theresa May could then trigger Article 50, which formally starts the Brexit process, as early as Tuesday.
Both the House of Commons and House of Lords will debate and vote on the bill on Monday. MPs will go first, and if they reverse the Lords changes it will be passed back to peers to decide whether they want to go against the government’s plans again.
The bill travels back and forth between the two chambers until both sides agree – Parliament could sit through the night to try to reach an agreement, and time has also been set aside on Tuesday and Wednesday.
Once it is agreed, the bill will go for Royal Assent, after which Mrs May can formally tell the rest of the EU that she is ready to start negotiating.