Proposals for reaching a new Brexit deal had been expected ahead of a crucial European Union summit (EU) on October 17, the BBC said in its report.
With the detailed proposals on the table, the UK side hopes that by the end of the week, both the EU and UK would be in a period of intense negotiations where both sides thrash out a final text.
But there was no certainty over whether the EU will accept the premise of the plans in order to move to the next phase of talks.
The biggest obstacle to a deal is the backstop - the plan to prevent a hard border between Northern Ireland and the Irish Republic.
The policy - agreed to by former Prime Minister Theresa May in her withdrawal deal with the EU, which was rejected three times by Parliament - is unacceptable to many Conservative MPs.
Since becoming Prime Minister, Boris Johnson has stressed to EU leaders the backstop would have to be replaced if any deal was to be passed by Parliament.
Johnson has argued that the backstop would keep the UK too closely aligned with EU rules after Brexit.
The UK is due to leave the EU on October 31, and Johnson has said this will happen whether or not there is a new deal with Brussels, the BBC reported.
At the Conservative Party conference on Monday, he said: "I'm cautiously optimistic. We have made some pretty big moves, we are waiting to see whether our European friends will help us and whether we can find the right landing zone."
MPs have passed a law requiring Johnson to seek an extension to the deadline from the bloc if he was unable to pass a deal in Parliament, or get MPs to approve a no-deal Brexit, by October 19.
( With inputs from IANS )