Confidential documents that “reflect the ideas the UK has put forward” on Brexit have been shared with the EU, the UK government has said.
Ministers will table “formal written solutions when we are ready” and not to an “artificial deadline”, it added.
Boris Johnson said he did not want to “exaggerate progress” of negotiations, but some was being made.
It comes after Finland’s prime minister said that Mr Johnson had 12 days to set out his Brexit plans to the EU.
But a government source said the development was not in response to the remarks.
Meanwhile, European Commission President Jean-Claude Juncker has told Sky News that talks earlier this week with Mr Johnson were “rather positive” and that a deal could be reached in the next few weeks.
Irish Taoiseach Leo Varadkar said he will try to get a deal with Mr Johnson when they meet at a UN summit in New York next week.
But his deputy, Simon Coveney, said there was “still a big gap” between what the UK government wanted and what Ireland and the EU needed, in terms of getting a deal.
The commission said it had received documents from the UK government and technical talks were taking place.
Chief spokesperson Mina Andreeva also confirmed there would be talks at a political level at a meeting on Friday between the EU’s chief negotiator, Michel Barnier, and Brexit Secretary Stephen Barclay.
The technical discussions were on some aspects of rules relating to customs and manufactured goods, as well as sanitary rules and phytosanitary rules – which relate to the health of plants – she said.
The BBC also understands “live discussions” are taking place between the EU and UK about ruling out another delay to Brexit if a deal is agreed.
Choice for MPs
Sources told BBC’s political editor Laura Kuenssberg that, if a plan is signed off by both sides, the EU could then announce it would not grant an extension to 31 October deadline if MPs voted the deal down – essentially giving them a choice between the negotiated deal or a no-deal Brexit.
Other sources on the EU and UK sides played down the possibility, denying there had been any formal consideration of the proposal and saying the current focus was on getting a deal.
But Laura Kuenssberg said: “It’s clear that government officials are considering ways of sticking to the prime minister’s October deadline, with, or without a deal being reached.”
Mr Johnson has said he wants to leave the EU, preferably with a deal, on 31 October and has urged the EU to scrap the backstop in the withdrawal agreement reached by predecessor Theresa May.
The backstop is the controversial policy aimed at preventing the return of a hard border on the island of Ireland and it was a key sticking point in Mrs May’s attempts to get Parliament to back her plan.
The EU has asked for alternative suggestions and had criticised the UK for not putting any plans in writing.
Mr Juncker told Sky News that the EU did not “need the backstop” if all its objectives for the Irish border were met.
He added that “if the results are there, I don’t care about the instruments”.
Mr Johnson said: “I don’t want to exaggerate the progress that we are making, but we are making progress.”
He said the UK needed to leave in a way that allowed it to “do things differently” and “not remain under the control of the EU in terms of laws and trade policy”.
But he also reiterated the need to ensure no hard border returned to Northern Ireland, and the Good Friday Agreement was protected.
“We think we can do that,” said the PM. “We think we can solve that problem and I think we are making some progress.”
He added: “Let’s see where we get. It is vital whatever happens that we prepare for no-deal and we will be ready for no-deal on 31 October. We have got to do both things at once.”
Earlier, Mr Rinne said he and French President Emmanuel Macron agreed the UK needed to produce the proposals in writing by the end of September, adding if not, “then it’s over”.
Finland currently holds the EU’s rotating presidency.
A French government official said the deadline was “not at all a new proposal” and added: “If we don’t get the proposals before the end of September, we will not have enough time to discuss them before the summit in October.”
The sending of the documents to the EU comes as the legal battle over the suspension of the UK Parliament is in its third day at the UK’s Supreme Court.
The UK government is arguing the decision to prorogue Parliament was a political matter and not for the courts to “design a set of rules” around it.
But campaigners say the move was used “for an improper purpose” – to stop MPs scrutinising Mr Johnson’s plans in the run up to Brexit on 31 October.
The prime minister prorogued Parliament earlier this month for five weeks, with MPs not scheduled to return until 14 October.