Jean-Claude Juncker, the head of the European Commission, said the chance of the UK and the EU reaching a deal has increased in the last few days and could be agreed by November.
Meanwhile, European Council President Donald Tusk said an agreement was possible by the end of 2018.
But Irish PM Leo Varadkar said there is still "a fair bit of work to be done".
The UK is due to leave the EU on 29 March 2019.
However, there is still no agreement on some issues, including how to avoid new checks on the Irish border.