Ashton and Tadic will continue dialogue over the phone today, Serbian newspapers said.
The Blic daily said the two officials would be in contact until a General Assembly meeting on Thursday.
Before the Ashton-Tadic meeting in Brussels, the European Union and Belgrade confirmed their readiness to work together on the text of the declaration so that it would be acceptable to both sides.
Nobody wants to see Serbia, the biggest country in the region, remaining defeated and instable. However, it is also necessary to accept the reality. It is clear to us that the ruling Democrats in Serbia must have something with which they can go before the electorate as their gain, the daily quoted an unnamed source from Brussels as saying.
Blic said that this should be the topic of dialogue between Belgrade and Pristina. It added that the EU and the United States had prepared an offer making it possible for Serbia to realise its important national interests without recognising Kosovo.