The Prime Minister will travel to Berlin to meet German Chancellor Angela Merkel on Wednesday, and meet French President Emmanuel Macron in Paris on Thursday, the BBC reported.
He is expected to tell the leaders that the UK Parliament cannot and will not change the outcome of the 2016 referendum and insist that there must be a new deal to replace his predecessor Theresa May's Withdrawal Agreement - which was defeated three times by MPs - if the country was to leave the EU with a deal.
Johnson in the past has insisted that the UK will leave the EU on October 31 with or without a deal.
However, Downing Street officials said that there would be "very little discussion" of Brexit during the meetings in France and Germany.
Meanwhile Labour leader Jeremy Corbyn has reiterated his call for MPs to work together to stop no-deal Brexit on October 31.
Speaking to the Observer daily on Sunday, Corbyn said his plan to be installed as a caretaker Prime Minister was the "simplest and most democratic way to stop no-deal".
The Labour leader has said he would delay Brexit, call a snap election, and campaign for another referendum as a caretaker Prime Minister.
More than 100 MPs from across the House of Commons have urged Johnson to recall Parliament and let it sit permanently until the UK leaves the EU.
( With inputs from IANS )