"We got on very well, it was a very useful, constructive conversation, a good start to the exercise," Davis told the BBC after the meeting.
The two counterparts met in Brussels earlier in the day, with Davis stating that they had made proposals on approaching the United Kingdom's withdrawal talks but did not hold any negotiations.
Davis stressed that an outcome where both the interests of the United Kingdom and the European Union were met was possible despite the two sides disagreeing over the freedom of movement and UK access to the EU single market.
On June 23, the United Kingdom voted on referendum to leave the European Union. UK Prime Minister Theresa May has stated that the country would trigger Article 50 by the end of March 2017, thus kick-starting withdrawal negotiations. The timing was later reaffirmed despite the High Court Ruling in November that the government must seek parliamentary approval before triggering the article.