BRUSSELS, Nov 1 (Reuters) - EU and British Brexit negotiators will continue talks in Brussels on Monday and until around mid-week, sources on both sides said on Sunday, in a sign both sides are still pushing to avoid a damaging trade rupture in less than nine weeks.

Intensive and secretive, the talks are a final bid to seal a new partnership agreement for when Britain's transition out of the European Union runs its course at the end of this year.

If the sides overcome their differences, the new deal would govern everything from trade and energy to transport and fisheries. If they fail, an estimated $900 billion of annual bilateral trade in goods and services would be damaged from Jan.1 by tariffs and quotas.

An EU diplomatic source and a UK official said negotiations would continue face-to-face in Brussels on Monday following a full weekend of talks. An update on their progress and the chances of a deal was expected on Wednesday or Thursday, they added. (Reporting by Gabriela Baczynska; Editing by Hugh Lawson)