European Council President Donald Tusk is proposing to offer the UK a 12-month "flexible" extension to its Brexit date, according to a senior EU source, the BBC reports.
His plan would allow the UK to leave sooner if Parliament ratifies a deal, but it would need to be agreed by EU leaders at a summit next week.
The UK's Conservatives and Labour Party are set to continue Brexit talks later.
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by MPs.
Downing Street said "technical" talks between Labour and the Conservatives on Thursday had been "productive" and would continue on Friday.