The development comes as rebel Conservatives and opposition Labour MPs are planning a bill to stop the UK leaving the European Union (EU) on October 31 without a deal, reports the BBC.
Conservative rebels have been warned they face expulsion from the party and de-selection if they support the cross-party legislation which would force the Prime Minister to ask for Brexit to be delayed until January 31, 2020, unless MPs had approved a new deal, or voted in favour of a no-deal exit, by October 19.
Under the Fixed Terms Parliament Act, Johnson would require the backing of two-thirds of the UK's 650 MPs to trigger a poll.
When Parliament returns on Tuesday after recess, they are expected to put forward the bill under Standing Order 24 - a rule that allows urgent debates to be heard.
In a televised announcement on Monday, Johnson insisted he could achieve changes to the UK's current Brexit deal at an EU summit on October 17.
But he said that if MPs voted to block the option of a no-deal Brexit they would "plainly chop the legs out from under the UK position" when he is negotiating.
Also on Tuesday, a judge in Edinburgh is due to hear arguments over the Johnson's plan to temporarily suspend the UK Parliament, the BBC reported.
The Prime Minister wants to suspend Parliament for five weeks ahead of a Queen's Speech on October 14.
A cross-party group of parliamentar wants a ruling at the Court of Session that Johnson was acting illegally.
( With inputs from IANS )