"We want to see a generous arrangement in terms of their right to remain and their treatment, just as we want to see a generous arrangement for British citizens around the EU," Davis said after meeting with Lithuania's Prime Minister Saulius Skvernelis on Tuesday.
In his words, efforts have been made in the past to discuss post-Brexit rights for migrants, however, representatives of some EU nations rejected the conversations, saying that the United Kingdom had not yet officially initiated the Brexit process. The launch is planned for late March.
Davis said the issue would have to be settled soon after the talks are opened to give people more clarity about their future.
"We want a generous outcome for everybody," said the Brexit minister.
According to data available to the Foreign Ministry, about 200,000 Lithuanians reside in the United Kingdom.
At least 1.2 million British citizens are estimated to be living and working in the other 27 EU member-states.