Barclay also said Britain had submitted the draft text of a new political declaration - one part of a Brexit deal with the European Union sets out the direction of a long term relationship with the bloc.
Against this background, Barclay confirmed to British MPs that Johnson would on Saturday comply with a United Kingdom law requiring him to send Brussels a letter calling for a Brexit delay if no deal was found.
This was partly because of objections to a proposal on customs from a small Northern Ireland political party whose votes Johnson will likely need to get a Brexit deal through parliament.
Pro-Brexit Conservative lawmaker David Davis said Wednesday that success rests on the stance of Northern Ireland's Democratic Unionist Party, the ally of Johnson's Conservative government.
Officials involved in the complex divorce between the world's fifth-largest economy and its biggest trading bloc said differences over the terms of the split from the 27 other member states had narrowed significantly.
Even if a deal is inked this week, moves in the British Parliament could still mean another delay to Britain's planned October 31 departure.
Brexit Secretary Steve Barclay said Wednesday that a draft text of a political declaration, one part of the Brexit deal with the European Union, had been submitted.
An EU official, who asked not to be identified because the negotiations were still ongoing, said Wednesday that "discussions continued until late in the night and will continue today".
British and European negotiators resumed intense negotiations on a draft Brexit deal Wednesday after late-night talks brought them closer but failed to confirm an elusive breakthrough.
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Kais Saied obtained 18.4 percent of votes whereas Nabil Karoui, then in prison but just released Wednesday, garnered 15.6 percent. The choice for voters between two quirky candidates who have never held political office has made for an unprecedented election.
Johnson won the top job by pledging to renegotiate May's agreement, though he is reviving the bulk of it now, with changes to the protocol on how to treat the border between European Union member Ireland and the British province of Northern Ireland.
The question is how to prevent the border becoming a backdoor into the EU's single market without erecting controls which could undermine the 1998 peace agreement that ended decades of conflict in the province.
"Talks have been constructive, but there still remains a number of significant issues to resolve", EU Commissioner Dimitris Avramopoulos said after being briefed by Barnier.
This is expected as Irish Prime Minister Leo Varadkar said that there were "many issues" to be resolved before a Brexit agreement could be reached.
But after Johnson's predecessor as prime minister, Theresa May, lost the Conservative Party's majority in Parliament in a 2017 election, she signed a deal with the DUP to prop up her minority government.
"The initial indications (from the EU) are that we are making progress, negotiations are moving in the right direction", he told reporters.
"But if it's not, there is still more time".
But Mr Barclay insisted the government was still committed to leaving on 31 October and when asked how he was planning to do so, responded: 'We will cross that bridge when we come to it'.