In a warning to potential Conservative rebels, a senior source from the whips office - which ensures MPs vote in line with the party - said on Sunday that rebels would "destroy" their Brexit negotiating position, the BBC reported.
The source said that any MP who failed to vote with the government would lose the party whip - meaning they would effectively be expelled from the party - and would not be able to stand as a Conservative candidate in an election.
The Conservatives have a majority of just one, including Northern Ireland's Democratic Unionist Party (DUP), so if any ruling party MP has the whip withdrawn they will go into a minority government.
The development comes as the opposition Labour Party's shadow cabinet will meet on Monday to finalise plans aimed at stopping a no-deal Brexit.
The UK is due to leave the European Union (EU) on October 31, with or without a deal.
Prime Minister Johnson has said that he was willing to leave without one rather than miss the deadline, which has prompted a number of MPs to unite to try to prevent a no-deal exit from the EU.
MPs will this week seek to bring forward a legislation against no deal in Parliament, with specific details expected to be outlined on Tuesday.
The source added on Sunday that if Conservative MPs fail to vote with the government on Tuesday "they will be destroying the government's negotiating position and handing control of Parliament to (Labour leader) Jeremy Corbyn".
Rebelling will be classed as voting against the government or abstaining, reports the BBC.
The whips office source said there was a chance of reaching a deal on October 17 - the date of the next EU summit - "only because Brussels realises the Prime Minister is totally committed to leaving on October 31".
( With inputs from IANS )