Writing in the Sunday Telegraph, Barnier said: "On the EU side, we had intense discussions with EU member states on the need to guarantee the integrity of the EU's single market, while keeping that border fully open.
"In this sense, the backstop is the maximum amount of flexibility that the EU can offer to a non-member state."
Barnier also said he was "not optimistic" about avoiding a no-deal Brexit, but "we should all continue to work with determination", the BBC reported.
"The EU is ready to explore all avenues that the UK government may present and that are compatible with the withdrawal agreement."
He added that the EU could not stop the UK from leaving without a deal, but he "would fail to understand the logic of that choice" because "we would still need to solve the same problems after October 31".
The backstop is part of the withdrawal agreement negotiated between Brussels and former Prime Minister Theresa May, which has been rejected by Parliament three times.
If implemented, it would see Northern Ireland staying aligned to some rules of the EU single market, should the UK and the EU not agree a trade deal after Brexit.
Johnson has said there has been some movement from the EU, as he attempts to broker a new deal and remove the arrangement, which he has described as "undemocratic".
The UK is due to leave the EU on 31 October, with or without a deal, reports the BBC.
The Prime Minister however, has said that he wants to leave the EU on October 31 with a deal, but it is "do or die" and was willing to leave without one rather than miss the deadline.
MPs opposed to a no-deal Brexit are expected to try and seize control of the Parliamentary agenda this week to push through legislation that would force the Prime Minister to seek a Brexit extension beyond October 31.
On Saturday, demonstrations were held across the UK in response to Johnson's plans to suspend Parliament in the run-up to Brexit.
The Prime Minister, who announced the move on August 28, said it would enable the government to bring forwards new legislation.
But the decision prompted an angry backlash from some politic and opponents of a no-deal Brexit.
( With inputs from IANS )