European relations minister Nick Thomas-Symonds told the BBC the UK was "pushing" for an agreement that would allow UK passport holders to use EU airport e-gates.
Thomas-Symonds said easing friction for British travellers was a "sensible objective" of the in-depth talks over the weekend. An announcement is expected on Monday (19 May) at a summit due to be held in London.
"I’m certainly pushing for people to be able to go through far more quickly," said Thomas-Symonds on Sunday (18 May).
"I think we can all agree not being stuck in queues and having more time to spend, whether it’s on holiday or work trips, having more time to do what you want would be a very sensible objective."
Since Brexit, UK passport holders have had to use a different, typically longer, queue at EU ports owing to the UK’s status now as a third country.
The proposed arrangement would allow British travellers to join the same queue as EU passport holders and to use e-gates, which is expected to reduce the time taken to complete checks.
Several countries have already started allowing this, such as Spain and Portugal.
However, arrivals will nonetheless still – separately – have to get their passports stamped and, once it’s live, have their fingerprints and face scanned (in lieu of passport stamping) once the EU’s new Entry-Exit System is live.